In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the no...In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann–Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover,the dynamical behaviour of the single-soliton solution is shown graphically.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
A chain of novel higher order rational solutions with some parameters and interaction solutions of a(2+1)-dimensional reverse space–time nonlocal Schrodinger(NLS)equation was derived by a generalized Darboux transfor...A chain of novel higher order rational solutions with some parameters and interaction solutions of a(2+1)-dimensional reverse space–time nonlocal Schrodinger(NLS)equation was derived by a generalized Darboux transformation(DT)which is derived by Taylor expansion and determinants.We obtained a series of higher-order rational solutions by one spectral parameter and we could get the periodic wave solution and three kinds of interaction solutions,singular breather and periodic wave interaction solution,singular breather and traveling wave interaction solution,bimodal breather and periodic wave interaction solution by two spectral parameters.We found a general formula for these solutions in the form of determinants.We also analyzed the complex wave structures of the dynamic behaviors and the effects of special parameters and presented exact solutions for the(2+1)-dimensional reverse space–time nonlocal NLS equation.展开更多
The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation an...The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further.On the other hand,the group invariant solutions of the SK equation are constructed with the classic Lie group method.In particular,by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.展开更多
Tis paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three- qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Merm...Tis paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three- qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Mermin Ardehali- Belinksii-Klyshko inequality is used to detect the degree of nonlocality, as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of the environment and the strength of the three-site interaction on the Bell-inequality violations are given. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by decoherence under certain conditions for the GHZ state. The decoherence-free subspaces of our model are identified and the entanglement of quantum states is also discussed.展开更多
The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method.The nonlocal symmetries a...The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method.The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables.The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly.Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.展开更多
Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:i...Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:incorporating nonlocal interactions into lattice beams,creating“nonlocal lattices”.Utilizing simulation experiments,we investigated the bending behaviors of these lattices,with a particular focus on their damage evolution.Interestingly,these nonlocal lattices,categorized as stretch-dominated,exhibit extraordinary peak force(strength)and stiffness(modulus)comparable to traditional stretchdominated lattices,while maintaining superior energy absorption(toughness).Analysis of damage evolution within the lattice beams reveals a transition from localized to dispersed damage patterns.This transition delays strain localization,thereby improving material utilization efficiency.Furthermore,stronger nonlocal interaction leads to a more dispersed damage zone,further improving materials utilization efficiency.These findings demonstrate that nonlocal lattices achieve excellent energy dissipation(toughness)without compromising strength and stiffness.This highlights the crucial role of nonlocal interactions in governing strain localization within lattice materials.The design strategy here unlocks new inspirations for the development of strong and tough lightweight materials.展开更多
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related...Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group Jnvariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.展开更多
We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is p...We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.展开更多
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for...The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.展开更多
Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the La...Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.展开更多
Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, mult...Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, multiple solitons, and soliton molecules of the ABSK systems are obtained via the bilinear method and the velocity resonant mechanism. Though the interactions among solitons are elastic, the interactions between soliton and soliton molecules are not elastic.In particular, the shapes of the soliton molecules are changed explicitly after interactions.展开更多
基于JUNG P S等提出的新型竞争非局域模型数值研究了艾里高斯光束在该模型中的相互作用,采用分步傅里叶算法数值模拟艾里高斯光束在竞争型非局域非线性向列相液晶中的相互作用。结果表明,可以通过调节初始振幅、初始间距、位相差以及非...基于JUNG P S等提出的新型竞争非局域模型数值研究了艾里高斯光束在该模型中的相互作用,采用分步傅里叶算法数值模拟艾里高斯光束在竞争型非局域非线性向列相液晶中的相互作用。结果表明,可以通过调节初始振幅、初始间距、位相差以及非局域程度控制艾里高斯光束间的相互作用。初始振幅增大会使相互作用力增大;分子取向非局域程度的增加导致艾里高斯光束宽度展宽,使反相艾里光束吸引力增强,热非局域程度的改变使初始振幅较大的反相艾里高斯光束由相互排斥作用变为相互吸引作用,使反相艾里高斯光束出现排斥和吸引作用动态平衡;同时还发现增大热非线性系数能使反相艾里高斯光束出现吸引或排斥。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11331008 and 11522112)
文摘In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann–Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover,the dynamical behaviour of the single-soliton solution is shown graphically.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
文摘A chain of novel higher order rational solutions with some parameters and interaction solutions of a(2+1)-dimensional reverse space–time nonlocal Schrodinger(NLS)equation was derived by a generalized Darboux transformation(DT)which is derived by Taylor expansion and determinants.We obtained a series of higher-order rational solutions by one spectral parameter and we could get the periodic wave solution and three kinds of interaction solutions,singular breather and periodic wave interaction solution,singular breather and traveling wave interaction solution,bimodal breather and periodic wave interaction solution by two spectral parameters.We found a general formula for these solutions in the form of determinants.We also analyzed the complex wave structures of the dynamic behaviors and the effects of special parameters and presented exact solutions for the(2+1)-dimensional reverse space–time nonlocal NLS equation.
基金supported by the National Natural Science Foundation of China,Grant No.11835011 and Grant No.11675146。
文摘The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further.On the other hand,the group invariant solutions of the SK equation are constructed with the classic Lie group method.In particular,by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.
基金Project supported by the National Natural Science Foundation of China (Grant No.11004050)the Scientific Research Fund of Hunan Provincial Education Department of China (Grant Nos.+3 种基金 09A013 and 10B013)the Science and Technology Research Foundation of Hunan Province of China (Grant No.2010FJ4120)the Excellent Talents Program of Hengyang Normal University of China (Grant No.2010YCJH01)the Science Foundation of Hengyang Normal University of China (Grant Nos.10A46 and 10B69)
文摘Tis paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three- qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Mermin Ardehali- Belinksii-Klyshko inequality is used to detect the degree of nonlocality, as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of the environment and the strength of the three-site interaction on the Bell-inequality violations are given. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by decoherence under certain conditions for the GHZ state. The decoherence-free subspaces of our model are identified and the entanglement of quantum states is also discussed.
基金supported by National Natural Science Foundation of China(No.11471215)Shanghai Natural Science Foundation(No.18ZR142600)。
文摘The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method.The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables.The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly.Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.
基金supported by the National Natural Science Foundation of China(Grant Nos.11932002 and 11902004).
文摘Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:incorporating nonlocal interactions into lattice beams,creating“nonlocal lattices”.Utilizing simulation experiments,we investigated the bending behaviors of these lattices,with a particular focus on their damage evolution.Interestingly,these nonlocal lattices,categorized as stretch-dominated,exhibit extraordinary peak force(strength)and stiffness(modulus)comparable to traditional stretchdominated lattices,while maintaining superior energy absorption(toughness).Analysis of damage evolution within the lattice beams reveals a transition from localized to dispersed damage patterns.This transition delays strain localization,thereby improving material utilization efficiency.Furthermore,stronger nonlocal interaction leads to a more dispersed damage zone,further improving materials utilization efficiency.These findings demonstrate that nonlocal lattices achieve excellent energy dissipation(toughness)without compromising strength and stiffness.This highlights the crucial role of nonlocal interactions in governing strain localization within lattice materials.The design strategy here unlocks new inspirations for the development of strong and tough lightweight materials.
基金Supported by the National Natural Science Foundations of China under Grant Nos. 11175092, 11275123, 11205092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y201017148K.C. Wong Magna Fund in Ningbo University
文摘Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group Jnvariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
基金Project supported by the National Natural Science Foundation of China(Nos.11972174 and 11672119)。
文摘We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.
基金Supported by the Global Change Research Program China under Grant No.2015CB953904the National Natural Science Foundations of China under Grant Nos.11435005,11175092,and 11205092+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.
基金supported by the Aviation Science Foundation of China (20080252006)
文摘Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.
文摘Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, multiple solitons, and soliton molecules of the ABSK systems are obtained via the bilinear method and the velocity resonant mechanism. Though the interactions among solitons are elastic, the interactions between soliton and soliton molecules are not elastic.In particular, the shapes of the soliton molecules are changed explicitly after interactions.
文摘基于JUNG P S等提出的新型竞争非局域模型数值研究了艾里高斯光束在该模型中的相互作用,采用分步傅里叶算法数值模拟艾里高斯光束在竞争型非局域非线性向列相液晶中的相互作用。结果表明,可以通过调节初始振幅、初始间距、位相差以及非局域程度控制艾里高斯光束间的相互作用。初始振幅增大会使相互作用力增大;分子取向非局域程度的增加导致艾里高斯光束宽度展宽,使反相艾里光束吸引力增强,热非局域程度的改变使初始振幅较大的反相艾里高斯光束由相互排斥作用变为相互吸引作用,使反相艾里高斯光束出现排斥和吸引作用动态平衡;同时还发现增大热非线性系数能使反相艾里高斯光束出现吸引或排斥。
