On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1...On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equatio...Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.展开更多
The low-dose X-ray induced long afterglow near infrared(NIR)luminescence from Cr^(3+)doped Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions was investigated.The structure analysis shows the good formation of Zn_(1-x)Cd...The low-dose X-ray induced long afterglow near infrared(NIR)luminescence from Cr^(3+)doped Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions was investigated.The structure analysis shows the good formation of Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions,which possesses a cubic spinel structure with Fd3m space group.The formation of Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions induces the obvious increase of long afterglow near infrared luminescence excited by low-dose X-ray,When the content of doped Cd^(2+)reaches 0.1,the low-dose X-ray induced long afterglow NIR luminescence is the maximum.More importantly,only 5 s Xray irradiation can induce more than 6 h NIR afterglow emission,of which the afterglow luminescent intensity is still 5 times stronger than the background intensity after 6 h.The thermoluminescent results show that under the 5 s exposure of X-ray,the trap density of Zn_(0.9)Cd_(0.1)Ga_(2)O_(4):Cr^(3+)is much higher than that of ZnGa_(2)O_(4):Cr^(3+).The replacement of Cd^(2+)ions with large radius at Zn^(2+)sites causes the increase of de fects and dislocations,which results in the obvious increase of trap co ncentrations.And the addition of high-z number elements Cd^(2+)would enhance the X-ray absorption of the solid solutions,which thus can be easily excited by low-dose X-ray.Zn_(0.9)Cd_(0.1)Ga_(2)O_(4):1%Cr^(3+)solid solution is a potential candidate of lowdose X-ray induced long afterglow luminescent materials.展开更多
Most studies have shown that oxygen vacancies on Ce_(x)Zr_(1-x)O_(2) solid solution are important for enhancing the catalytic oxidation performance.However,a handful of studies investigated the different roles of surf...Most studies have shown that oxygen vacancies on Ce_(x)Zr_(1-x)O_(2) solid solution are important for enhancing the catalytic oxidation performance.However,a handful of studies investigated the different roles of surface and subsurface oxygen vacancies on the performance and mechanisms of catalysts.Herein,a series of zirconium doping on CeO_(2) samples(CeO_(2),Ce_(0.95)Zr_(0.05)O_(2),and Ce_(0.8)5Zr_(0.15)O_(2))with various surface-to-subsurface oxygen vacancies ratios have been synthesized and applied in toluene catalytic oxidation.The obtained Ce_(0.95)Zr_(0.05)O_(2) exhibits an excellent catalytic performance with a 90%toluene conversion at 295℃,which is 68℃lower than that of CeO_(2).Additionally,the obtained Ce_(0.95)Zr_(0.05)O_(2)catalyst also exhibited good catalytic stability and water resistance.The XRD and HRTEM results show that Zr ions are incorporated into CeO_(2) lattice,forming Ce_(x)Zr_(1-x)O_(2) solid solution.Temperature-programmed experiments reveal that Ce_(0.95)Zr_(0.05)O_(2) shows excellent lowtemperature reducibility and abundant surface oxygen species.In-situ DRIFTS tests were used to probe the reaction mechanism,and the function of Zr doping in promoting the activation of oxygen was further determined.Density functional theory(DFT)calculations indicate that the vacancy formation energy and O_(2) adsorption energy are both lower on Ce_(0.95)Zr_(0.05)O_(2),confirming the reason for its superior catalytic performance.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
In this paper,we mainly focus on proving the existence of lump solutions to a generalized(3+1)-dimensional nonlinear differential equation.Hirota’s bilinear method and a quadratic function method are employed to deri...In this paper,we mainly focus on proving the existence of lump solutions to a generalized(3+1)-dimensional nonlinear differential equation.Hirota’s bilinear method and a quadratic function method are employed to derive the lump solutions localized in the whole plane for a(3+1)-dimensional nonlinear differential equation.Three examples of such a nonlinear equation are presented to investigate the exact expressions of the lump solutions.Moreover,the 3d plots and corresponding density plots of the solutions are given to show the space structures of the lump waves.In addition,the breath-wave solutions and several interaction solutions of the(3+1)-dimensional nonlinear differential equation are obtained and their dynamics are analyzed.展开更多
A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlev...A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlevéexpansion method.Subsequently,the residue symmetry is localized to a Lie point symmetry of a prolonged system,from which the finite transformation group is derived.Secondly,the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion solvability.Simultaneously,explicit soliton-cnoidal wave solutions are provided.Finally,abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.展开更多
Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generator...Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.展开更多
Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresp...Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.展开更多
Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）-...Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.展开更多
In this paper,we report the deductive formula used for the method of dual-wavelength corresponding solutions under condition of having ligand interference and the stability constants of three new coordination compound...In this paper,we report the deductive formula used for the method of dual-wavelength corresponding solutions under condition of having ligand interference and the stability constants of three new coordination compounds [AuL_2]^+determined with this method.The stability of the three compounds,the necessity of controlling pH in experimental systems and the advantage of this method are discussed in detail.展开更多
In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational lo...In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.展开更多
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral fo...A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.展开更多
AIM: To investigate the benefits of insulin like growth factor-1 (IGF-1) supplementation to serum-free institut georges lopez-1 (IGL-1) solution to protect fatty liver against cold ischemia reperfusion injury. METHO...AIM: To investigate the benefits of insulin like growth factor-1 (IGF-1) supplementation to serum-free institut georges lopez-1 (IGL-1) solution to protect fatty liver against cold ischemia reperfusion injury. METHODS: Steatotic livers were preserved for 24 h in IGL-1 solution supplemented with or without IGF-1 and then perfused "ex vivo " for 2 h at 37℃. We examined the effects of IGF-1 on hepatic damage and function (transaminases, percentage of sulfobromophthalein clearance in bile and vascular resistance). We also studied other factors associated with the poor tolerance of fatty livers to cold ischemia reperfusion injury such as mitochondrial damage, oxidative stress, nitric oxide, tumor necrosis factor-α (TNF-α) and mitogen-activated protein kinases.RESULTS: Steatotic livers preserved in IGL-1 solutionsupplemented with IGF-1 showed lower transaminase levels, increased bile clearance and a reduction in vascular resistance when compared to those preserved in IGL-1solution alone. These benefits are mediated by activation of AKT and constitutive endothelial nitric oxide synthase (eNOS), as well as the inhibition of inflammatory cytokines such as TNF-α. Mitochondrial damage and oxidative stress were also prevented.CONCLUSION: IGL-1 enrichment with IGF-1 increasedfatty liver graft preservation through AKT and eNOS activation, and prevented TNF-α release during normothermic reperfusion.展开更多
The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is present...The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.展开更多
In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized...In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.展开更多
基金supported by the National Natural Science Foundation of China(11931009,12271495,11971450,and 12071449)Anhui Initiative in Quantum Information Technologies(AHY150200)the Project of Stable Support for Youth Team in Basic Research Field,Chinese Academy of Sciences(YSBR-001).
文摘On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.
基金Project supported by the State Key Research Project of Shandong Natural Science Foundation(ZR2020KB019)the fund of"Two-Hundred Talent"Plan of Yantai City+1 种基金the National Natural Science Foundation of China(11974013)the Natural Science Foundation of Fujian Province(2022J011270)。
文摘The low-dose X-ray induced long afterglow near infrared(NIR)luminescence from Cr^(3+)doped Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions was investigated.The structure analysis shows the good formation of Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions,which possesses a cubic spinel structure with Fd3m space group.The formation of Zn_(1-x)Cd_(x)Ga_(2)O_(4)spinel solid solutions induces the obvious increase of long afterglow near infrared luminescence excited by low-dose X-ray,When the content of doped Cd^(2+)reaches 0.1,the low-dose X-ray induced long afterglow NIR luminescence is the maximum.More importantly,only 5 s Xray irradiation can induce more than 6 h NIR afterglow emission,of which the afterglow luminescent intensity is still 5 times stronger than the background intensity after 6 h.The thermoluminescent results show that under the 5 s exposure of X-ray,the trap density of Zn_(0.9)Cd_(0.1)Ga_(2)O_(4):Cr^(3+)is much higher than that of ZnGa_(2)O_(4):Cr^(3+).The replacement of Cd^(2+)ions with large radius at Zn^(2+)sites causes the increase of de fects and dislocations,which results in the obvious increase of trap co ncentrations.And the addition of high-z number elements Cd^(2+)would enhance the X-ray absorption of the solid solutions,which thus can be easily excited by low-dose X-ray.Zn_(0.9)Cd_(0.1)Ga_(2)O_(4):1%Cr^(3+)solid solution is a potential candidate of lowdose X-ray induced long afterglow luminescent materials.
基金supported by the National Natural Science Foundation(No.51678291)the Basic Science(Natural Science)Research in Higher Education in Jiangsu Province(No.23KJA610003)the High-level Scientific Research Foundation for the introduction of talent in Nanjing Institute of Technology(No.YKJ201999)。
文摘Most studies have shown that oxygen vacancies on Ce_(x)Zr_(1-x)O_(2) solid solution are important for enhancing the catalytic oxidation performance.However,a handful of studies investigated the different roles of surface and subsurface oxygen vacancies on the performance and mechanisms of catalysts.Herein,a series of zirconium doping on CeO_(2) samples(CeO_(2),Ce_(0.95)Zr_(0.05)O_(2),and Ce_(0.8)5Zr_(0.15)O_(2))with various surface-to-subsurface oxygen vacancies ratios have been synthesized and applied in toluene catalytic oxidation.The obtained Ce_(0.95)Zr_(0.05)O_(2) exhibits an excellent catalytic performance with a 90%toluene conversion at 295℃,which is 68℃lower than that of CeO_(2).Additionally,the obtained Ce_(0.95)Zr_(0.05)O_(2)catalyst also exhibited good catalytic stability and water resistance.The XRD and HRTEM results show that Zr ions are incorporated into CeO_(2) lattice,forming Ce_(x)Zr_(1-x)O_(2) solid solution.Temperature-programmed experiments reveal that Ce_(0.95)Zr_(0.05)O_(2) shows excellent lowtemperature reducibility and abundant surface oxygen species.In-situ DRIFTS tests were used to probe the reaction mechanism,and the function of Zr doping in promoting the activation of oxygen was further determined.Density functional theory(DFT)calculations indicate that the vacancy formation energy and O_(2) adsorption energy are both lower on Ce_(0.95)Zr_(0.05)O_(2),confirming the reason for its superior catalytic performance.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
基金supported by the National Natural Science Foundation of China(Nos.12101572,12371256)2023 Shanxi Province Graduate Innovation Project(No.2023KY614)the 19th Graduate Science and Technology Project of North University of China(No.20231943)。
文摘In this paper,we mainly focus on proving the existence of lump solutions to a generalized(3+1)-dimensional nonlinear differential equation.Hirota’s bilinear method and a quadratic function method are employed to derive the lump solutions localized in the whole plane for a(3+1)-dimensional nonlinear differential equation.Three examples of such a nonlinear equation are presented to investigate the exact expressions of the lump solutions.Moreover,the 3d plots and corresponding density plots of the solutions are given to show the space structures of the lump waves.In addition,the breath-wave solutions and several interaction solutions of the(3+1)-dimensional nonlinear differential equation are obtained and their dynamics are analyzed.
基金supported by the National Natural Science Foundation of China(No.12375006).
文摘A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlevéexpansion method.Subsequently,the residue symmetry is localized to a Lie point symmetry of a prolonged system,from which the finite transformation group is derived.Secondly,the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion solvability.Simultaneously,explicit soliton-cnoidal wave solutions are provided.Finally,abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.
文摘Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.
基金supported by the National Natural Science Foundation of China (Grant Nos.12275085 and 12235007)the Science and Technology Commission of Shanghai Municipality (Grant No.22DZ2229014)。
文摘Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.
基金supported by the Natural Science Foundation of Shandong Province of China under Grant Nos.Q2005A01
文摘Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.
文摘In this paper,we report the deductive formula used for the method of dual-wavelength corresponding solutions under condition of having ligand interference and the stability constants of three new coordination compounds [AuL_2]^+determined with this method.The stability of the three compounds,the necessity of controlling pH in experimental systems and the advantage of this method are discussed in detail.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11675054 and 11435005+1 种基金Outstanding Doctoral Dissertation Cultivation Plan of Action under Grant No.YB2016039Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.
文摘A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.
基金Supported by The Ministry of Health and Consumption(PI081988),CIBER-ehd,Carlos Ⅲ Institute,Madrid,SpainMinistry of Foreign Affairs and International Cooperation(A/020255/08and A/02987/09)Mohamed Amine Zaouali is fellowship-holder from the Catalan Society of Transplantation
文摘AIM: To investigate the benefits of insulin like growth factor-1 (IGF-1) supplementation to serum-free institut georges lopez-1 (IGL-1) solution to protect fatty liver against cold ischemia reperfusion injury. METHODS: Steatotic livers were preserved for 24 h in IGL-1 solution supplemented with or without IGF-1 and then perfused "ex vivo " for 2 h at 37℃. We examined the effects of IGF-1 on hepatic damage and function (transaminases, percentage of sulfobromophthalein clearance in bile and vascular resistance). We also studied other factors associated with the poor tolerance of fatty livers to cold ischemia reperfusion injury such as mitochondrial damage, oxidative stress, nitric oxide, tumor necrosis factor-α (TNF-α) and mitogen-activated protein kinases.RESULTS: Steatotic livers preserved in IGL-1 solutionsupplemented with IGF-1 showed lower transaminase levels, increased bile clearance and a reduction in vascular resistance when compared to those preserved in IGL-1solution alone. These benefits are mediated by activation of AKT and constitutive endothelial nitric oxide synthase (eNOS), as well as the inhibition of inflammatory cytokines such as TNF-α. Mitochondrial damage and oxidative stress were also prevented.CONCLUSION: IGL-1 enrichment with IGF-1 increasedfatty liver graft preservation through AKT and eNOS activation, and prevented TNF-α release during normothermic reperfusion.
基金Supported by the International Cooperation and Exchanges Foundation of Henan Province (084300510060)the Youth Science Foundation of Henan University of Science and Technology of China (2008QN026)
文摘The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013QNA41Natural Sciences Foundation of China under Grant Nos.11301527 and 11371361the Construction Project of the Key Discipline in Universities for 12th Five-year Plans by Jiangsu Province
文摘In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.
