We used observed concentrations of air pollutants,reanalyzed meteorological parameters,and results from the Goddard Earth Observing System Chemical Transport Model to examine the relationships between concentrations o...We used observed concentrations of air pollutants,reanalyzed meteorological parameters,and results from the Goddard Earth Observing System Chemical Transport Model to examine the relationships between concentrations of maximum daily 8-h average ozone(MDA8 O_(3)),PM_(2.5)(particulate matter with diameter of 2.5μm or less),and PM_(2.5)components and 2-m temperature(T2)or relative humidity(RH),as well as the effectiveness of precursor emission reductions on the control of O_(3) and PM_(2.5) in Beijing–Tianjin–Hebei(BTH)under different summertime temperature and humidity conditions.Both observed(simulated)MDA8 O_(3) and PM_(2.5) concentrations increased as T2 went up,with linear trends of 4.8(3.2)ppb℃^(−1) and 1.9(1.5)μg m^(−3)℃^(−1),respectively.Model results showed that the decreases in MDA8 O_(3) from precursor emission reductions were more sensitive to T2 than to RH.Reducing a larger proportion of volatile organic compound(VOC)emissions at higher T2 was more effective for the control of summertime O_(3) in BTH.For the control of summertime PM_(2.5) in BTH,reducing nitrogen oxides(NOx)combined with a small proportion of VOCs was the best measure.The magnitude of reduction in PM_(2.5) from reducing precursor emissions was more sensitive to RH than to T2,with the best efficiency at high RH.Results from this study are helpful for formulating effective policies to tackle O_(3) and PM_(2.5) pollution in BTH.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
To guarantee the blue skies for the 2022 Winter Olympics held in Beijing and Zhangjiakou from February 4 to 20,Beijing and its surrounding areas adopted a series of emission control measures.This provides an opportuni...To guarantee the blue skies for the 2022 Winter Olympics held in Beijing and Zhangjiakou from February 4 to 20,Beijing and its surrounding areas adopted a series of emission control measures.This provides an opportunity to determine the impacts of large-scale temporary control measures on the air quality in Beijing during this special period.Here,we applied the WRF-CMAQ model to quantify the contributions of emission reduction measures and meteorological conditions.Results show that meteorological conditions in 2022 decreased PM_(2.5)in Beijing by 6.9 and 11.8μg/m^(3)relative to 2021 under the scenarios with and without emission reductions,respectively.Strict emission reduction measures implemented in Beijing and seven neighboring provinces resulted in an average decrease of 13.0μg/m^(3)(-41.2%)in PM_(2.5)in Beijing.Over the entire period,local emission reductions contributed more to good air quality in Beijing than nonlocal emission reductions.Under the emission reduction scenario,local,controlled regions,other regions,and boundary conditions contributed 47.7%,42.0%,5.3%,and 5.0%to the PM_(2.5)concentrations in Beijing,respectively.The results indicate that during the cleaning period with the air masses from the northwest,the abatements of PM_(2.5)were mainly caused by local emission reductions.However,during the potential pollution period with the air masses from the east-northeast and west-southwest,the abatements of PM_(2.5)were caused by both local and nonlocal emission reductions almost equally.This implies that regional coordinated prevention and control strategies need to be arranged scientifically and rationally when heavy pollution events are forecasted.展开更多
The Yangtze River Economic Belt(YREB)is a pivotal contributor to China's economic growth,particularly as the nation undergoes a green transformation.Achieving synergistic reductions on pollution and carbon emissio...The Yangtze River Economic Belt(YREB)is a pivotal contributor to China's economic growth,particularly as the nation undergoes a green transformation.Achieving synergistic reductions on pollution and carbon emissions is deemed crucial for this transition.This paper examines the spatial and temporal changes in the synergy of pollution and carbon reduction in the YREB and delves into the underlying mechanisms.Our findings indicate that while the synergy in the YREB is increasing,it manifests disparities across regions,with the lower reaches outperforming the middle and upper ones.Enterprise behavior,government guidance,and regional endowments influence this synergy.Cities in the YREB must strategically plan their urban scale,curb population overgrowth,recalibrate their industrial structures,curtail energy consumption,and enhance policy efficacy.Distinct regions should prioritize various objectives:the lower reaches should hasten scientific advancements and technological innovations;the middle reaches should foster innovation and industrial upgrades;and the upper reaches should prioritize rural and urban land intensification.展开更多
Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation al...Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.展开更多
In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, ...In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.展开更多
The homogeneous balance method, which is simple and straightforward, is extended to seek for Backlund transformation, exact bell shape soliton solutions and similarity reduction of the Boussinesq equation. The method...The homogeneous balance method, which is simple and straightforward, is extended to seek for Backlund transformation, exact bell shape soliton solutions and similarity reduction of the Boussinesq equation. The method can be used in general.展开更多
Contingent Valuation Method(CVM) was used to investigate the Chinese public's willingness to pay(WTP) for a policy to reduce CO2 emissions. Face to face interviews were conducted to collect 1,653 valid questionnai...Contingent Valuation Method(CVM) was used to investigate the Chinese public's willingness to pay(WTP) for a policy to reduce CO2 emissions. Face to face interviews were conducted to collect 1,653 valid questionnaires from Beijing, Shanghai, Shandong province, and Fujian province. A model was constructed to understand the factors that influence WTP. The results indicate that the Chinese public is willing to pay CN 201.86 annually to support the policy of reducing greenhouse gas emissions. Participants from Beijing show the highest WTP, followed by participants from Fujian and Shandong, while those from Shanghai report the lowest WTP. The findings reveal that participants with higher income, higher satisfaction with their current life, and awareness of climate issues are willing to pay more for CO2 emissions reductions. In addition, those who are young, male and members of the Communist Party also indicate a higher WTP. The results imply that translating the public's willingness to protect climate into actions should be taken into account in China's low carbon policy. There is a need to consider the difference in degree of willingness, among different social groups, to pay for emissions reductions if the market-based mechanisms such as carbon tax were designed to facilitate emissions reductions.展开更多
As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivativ...As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.展开更多
Using Ablowitz-Ramani Segur algorithm, the coupled KdV systems are reclassified under the Painlevé integrable sense while the similarity reductions of the model are obtained by using the Clarkson and Kruskal＇s d...Using Ablowitz-Ramani Segur algorithm, the coupled KdV systems are reclassified under the Painlevé integrable sense while the similarity reductions of the model are obtained by using the Clarkson and Kruskal＇s direct method. Some new types of Painlevé integrable models including a model with different dispersion relations for two layer fluids are found.展开更多
A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the non...A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.展开更多
The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corre...The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.展开更多
For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each...For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each class, and someexamples of exact invainvariant solutions are given.展开更多
Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented i...Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.展开更多
Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differentia...Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.展开更多
Basing on the direct method developed by Clarkson and Kruskal,the nonisospectral BKP equation can bereduced to three types of(1+1)-dimensional variable coefficients partial differential equations(PDEs).Furthermore,ont...Basing on the direct method developed by Clarkson and Kruskal,the nonisospectral BKP equation can bereduced to three types of(1+1)-dimensional variable coefficients partial differential equations(PDEs).Furthermore,onthe basis of the idea of the symmetry group direct method by Lou et al.,three types of reduction PDEs are all reducedto the related constant coefficients PDEs by some transformations.展开更多
The （2＋1）-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-di...The （2＋1）-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.展开更多
It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is natu...It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.展开更多
The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé...The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.91744311).
文摘We used observed concentrations of air pollutants,reanalyzed meteorological parameters,and results from the Goddard Earth Observing System Chemical Transport Model to examine the relationships between concentrations of maximum daily 8-h average ozone(MDA8 O_(3)),PM_(2.5)(particulate matter with diameter of 2.5μm or less),and PM_(2.5)components and 2-m temperature(T2)or relative humidity(RH),as well as the effectiveness of precursor emission reductions on the control of O_(3) and PM_(2.5) in Beijing–Tianjin–Hebei(BTH)under different summertime temperature and humidity conditions.Both observed(simulated)MDA8 O_(3) and PM_(2.5) concentrations increased as T2 went up,with linear trends of 4.8(3.2)ppb℃^(−1) and 1.9(1.5)μg m^(−3)℃^(−1),respectively.Model results showed that the decreases in MDA8 O_(3) from precursor emission reductions were more sensitive to T2 than to RH.Reducing a larger proportion of volatile organic compound(VOC)emissions at higher T2 was more effective for the control of summertime O_(3) in BTH.For the control of summertime PM_(2.5) in BTH,reducing nitrogen oxides(NOx)combined with a small proportion of VOCs was the best measure.The magnitude of reduction in PM_(2.5) from reducing precursor emissions was more sensitive to RH than to T2,with the best efficiency at high RH.Results from this study are helpful for formulating effective policies to tackle O_(3) and PM_(2.5) pollution in BTH.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by the National Natural Science Foundation of China (Nos.42175084,21577126,and 41561144004)the Department of Science and Technology of China (Nos.2018YFC0213506,2018YFC0213503,and 2016YFC0202702)+4 种基金the National Research Program for Key Issues in Air Pollution Control in China (No.DQGG0107)supported by the“Zhejiang 1000 Talent Plan”and Research Center for Air Pollution and Health in Zhejiang UniversityPengfei Li is supported by the National Natural Science Foundation of China (No.22006030)the Initiation Fund for Introducing Talents of Hebei Agricultural University (No.412201904)the Hebei Youth Top Q15 Fund (No.BJ2020032)。
文摘To guarantee the blue skies for the 2022 Winter Olympics held in Beijing and Zhangjiakou from February 4 to 20,Beijing and its surrounding areas adopted a series of emission control measures.This provides an opportunity to determine the impacts of large-scale temporary control measures on the air quality in Beijing during this special period.Here,we applied the WRF-CMAQ model to quantify the contributions of emission reduction measures and meteorological conditions.Results show that meteorological conditions in 2022 decreased PM_(2.5)in Beijing by 6.9 and 11.8μg/m^(3)relative to 2021 under the scenarios with and without emission reductions,respectively.Strict emission reduction measures implemented in Beijing and seven neighboring provinces resulted in an average decrease of 13.0μg/m^(3)(-41.2%)in PM_(2.5)in Beijing.Over the entire period,local emission reductions contributed more to good air quality in Beijing than nonlocal emission reductions.Under the emission reduction scenario,local,controlled regions,other regions,and boundary conditions contributed 47.7%,42.0%,5.3%,and 5.0%to the PM_(2.5)concentrations in Beijing,respectively.The results indicate that during the cleaning period with the air masses from the northwest,the abatements of PM_(2.5)were mainly caused by local emission reductions.However,during the potential pollution period with the air masses from the east-northeast and west-southwest,the abatements of PM_(2.5)were caused by both local and nonlocal emission reductions almost equally.This implies that regional coordinated prevention and control strategies need to be arranged scientifically and rationally when heavy pollution events are forecasted.
基金National Natural Science Foundation of China,No.42371318。
文摘The Yangtze River Economic Belt(YREB)is a pivotal contributor to China's economic growth,particularly as the nation undergoes a green transformation.Achieving synergistic reductions on pollution and carbon emissions is deemed crucial for this transition.This paper examines the spatial and temporal changes in the synergy of pollution and carbon reduction in the YREB and delves into the underlying mechanisms.Our findings indicate that while the synergy in the YREB is increasing,it manifests disparities across regions,with the lower reaches outperforming the middle and upper ones.Enterprise behavior,government guidance,and regional endowments influence this synergy.Cities in the YREB must strategically plan their urban scale,curb population overgrowth,recalibrate their industrial structures,curtail energy consumption,and enhance policy efficacy.Distinct regions should prioritize various objectives:the lower reaches should hasten scientific advancements and technological innovations;the middle reaches should foster innovation and industrial upgrades;and the upper reaches should prioritize rural and urban land intensification.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12235007, 11975131, and 12275144)the K. C. Wong Magna Fund in Ningbo Universitythe Natural Science Foundation of Zhejiang Province of China (Grant No. LQ20A010009)
文摘Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.
基金Natural Science Foundation of Shandong Province under Grant Nos.2004zx16 and Q2005A01
文摘In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.
文摘The homogeneous balance method, which is simple and straightforward, is extended to seek for Backlund transformation, exact bell shape soliton solutions and similarity reduction of the Boussinesq equation. The method can be used in general.
基金supported by the Foundation of the Humanities and Social Science, Ministry of Education of the People’s Republic of China (No. 09YJA790119)
文摘Contingent Valuation Method(CVM) was used to investigate the Chinese public's willingness to pay(WTP) for a policy to reduce CO2 emissions. Face to face interviews were conducted to collect 1,653 valid questionnaires from Beijing, Shanghai, Shandong province, and Fujian province. A model was constructed to understand the factors that influence WTP. The results indicate that the Chinese public is willing to pay CN 201.86 annually to support the policy of reducing greenhouse gas emissions. Participants from Beijing show the highest WTP, followed by participants from Fujian and Shandong, while those from Shanghai report the lowest WTP. The findings reveal that participants with higher income, higher satisfaction with their current life, and awareness of climate issues are willing to pay more for CO2 emissions reductions. In addition, those who are young, male and members of the Communist Party also indicate a higher WTP. The results imply that translating the public's willingness to protect climate into actions should be taken into account in China's low carbon policy. There is a need to consider the difference in degree of willingness, among different social groups, to pay for emissions reductions if the market-based mechanisms such as carbon tax were designed to facilitate emissions reductions.
基金the National Natural Science Foundation of China(Grant No.11975143)。
文摘As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.
基金National Natural Science Foundations of China under Grant Nos.10475055 and 40305009
文摘Using Ablowitz-Ramani Segur algorithm, the coupled KdV systems are reclassified under the Painlevé integrable sense while the similarity reductions of the model are obtained by using the Clarkson and Kruskal＇s direct method. Some new types of Painlevé integrable models including a model with different dispersion relations for two layer fluids are found.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675084 and 11435005Ningbo Natural Science Foundation under Grant No.2015A610159+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.
基金supported by National Natural Science Foundation of China under Grant Nos.10475055 and 90503006
文摘The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.
基金supported by the Natural science foundation of China(NSF),under grand number 11071159.
文摘For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each class, and someexamples of exact invainvariant solutions are given.
基金The project supported by the Alexander von Humboldt Foundationthe Youth Foundation of Shanghai Jiao Tong UniversityNational Natural Science Foundation of China under Grant No.10475055
文摘Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.
基金Supported by K.C. Wong Magna Fund in Ningbo University, NSF of China under Grant Nos. 10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408the Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093
文摘Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.
基金Supported by National Natural Science Foundation of China under Grant Nos.10747141 and 10735030Zhejiang Provincial Natural Science Foundations under Grant No.605408+2 种基金Ningbo Natural Science Foundation under Grant Nos.2007A610049 and 2008A610017National Basic Research Program of China (973 Program 2007CB814800)K.C.Wong Magna Fund in Ningbo University
文摘Basing on the direct method developed by Clarkson and Kruskal,the nonisospectral BKP equation can bereduced to three types of(1+1)-dimensional variable coefficients partial differential equations(PDEs).Furthermore,onthe basis of the idea of the symmetry group direct method by Lou et al.,three types of reduction PDEs are all reducedto the related constant coefficients PDEs by some transformations.
基金The project supported by National Natural Science Foundation of China under Grant No. 40333030, the Program for New Century Excellent Talents in Universities （NCET-05-0591）, the Shanghai Post-doctoral Foundation under Grant No. 06R214139, and the Shandong Taishan Scholar Foundation
文摘The （2＋1）-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.
基金Supported by NRF South Africathe National Natural Science Foundation of China(Grant No.11161032)
文摘It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975131 and 11435005)the K C Wong Magna Fund in Ningbo University。
文摘The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.
