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
2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper o...2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.展开更多
In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the （3＋1）- dimensional Kadomtsev Petviashvili （KP） equation. We find that the maximum amplitude of the res...In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the （3＋1）- dimensional Kadomtsev Petviashvili （KP） equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.展开更多
By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including t...By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.展开更多
By using Xu's stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili equations.These parameter functions make...By using Xu's stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili equations.These parameter functions make our solutions more applicable to related practical models and boundary value problems.展开更多
The famous Kadomtsev-Petviashvili(KP)equation 1 s a classical equation In soliton tneory.A Backlund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painl...The famous Kadomtsev-Petviashvili(KP)equation 1 s a classical equation In soliton tneory.A Backlund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlev6 expansion in this paper.One-parameter group transformations and one-parameter subgroup-invariant solutions for the extended KP equation are obtained.The consistent Riccati expansion(CRE) solvability of the KP equation is proved.Some interaction structures between soliton-cnoidal waves are obtained by CRE and several evolution graphs and density graphs are plotted.展开更多
Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechan...Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.展开更多
One- and two-periodic wave solutions for （3＋l）-dimensional Boussinesq equation are presented by means of Hirota＇s bilinear method and the Riemann theta function. The soliton solution can be obtained from the perio...One- and two-periodic wave solutions for （3＋l）-dimensional Boussinesq equation are presented by means of Hirota＇s bilinear method and the Riemann theta function. The soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.展开更多
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi...Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.展开更多
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supported by the National Key Basic Research Project of China (Grant No 2004CB318000)the National Natural Science Foundation of China (Grant No 10771072)+1 种基金the PhD Program Scholarship Fund of ECNU2008 (Grant No 20080052)the Youth Foundation of Inner Mongolia Normal University, China (Grant No QN07035)
文摘2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.
基金Project supported by the National Natural Science Foundation of China(Grant No.10575082)the Key Project Foundation of the Education Ministry of China(Grant No.209128)the Natural Science Foundation of Northwest Normal University(Grant No.NWNU-KJCXGC-03-53)
文摘In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the （3＋1）- dimensional Kadomtsev Petviashvili （KP） equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.
基金supported by National Natural Science Foundation of China (Grant Nos.10735030 and 40775042)Ningbo Natural Science Foundation (Grant No. 2008A610017)+1 种基金National Basic Research Program of China (973 Program) (Grant Nos. 2005CB422301 and 2007CB814800)K.C. Wong Magna Fund in Ningbo University
文摘By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.
基金Foundation item： Supported by the Program of Shannxi Provincial Department of Education（11JK0482） Supported by the NSF of China（11101332） Supported by the Natural Science Foundation of Henan Province （2007140020）
文摘By using Xu's stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili equations.These parameter functions make our solutions more applicable to related practical models and boundary value problems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11775047,11775146,and 11865013)the Science and Technology Project Foundation of Zhongshan City,China(Grant No.2017B1016).
文摘The famous Kadomtsev-Petviashvili(KP)equation 1 s a classical equation In soliton tneory.A Backlund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlev6 expansion in this paper.One-parameter group transformations and one-parameter subgroup-invariant solutions for the extended KP equation are obtained.The consistent Riccati expansion(CRE) solvability of the KP equation is proved.Some interaction structures between soliton-cnoidal waves are obtained by CRE and several evolution graphs and density graphs are plotted.
基金Supported by the National Natural Science Foundation of China under Grant 61072145the Scientific Research Project of Beijing Educational Committee(SQKM201211232016)Beijing Excellent Talent Training Project(2013D005007000003)
基金Project supported by the Natural Science Foundation of Guangdong Province of China (Grant No.10452840301004616)the National Natural Science Foundation of China (Grant No.61001018)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (Grant No.408YKQ09)
文摘Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.
文摘One- and two-periodic wave solutions for （3＋l）-dimensional Boussinesq equation are presented by means of Hirota＇s bilinear method and the Riemann theta function. The soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11505154,11605156,11775146,and 11975204)the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ16A010003 and LY19A050003)+5 种基金the China Scholarship Council(Grant No.201708330479)the Foundation for Doctoral Program of Zhejiang Ocean University(Grant No.Q1511)the Natural Science Foundation(Grant No.DMS-1664561)the Distinguished Professorships by Shanghai University of Electric Power(China)North-West University(South Africa)King Abdulaziz University(Saudi Arabia)
文摘Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.
