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
This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé...This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.展开更多
Fusion and fission are two important phenomena that have been experimentally observed in many real physical models.In this paper,we investigate the two phenomena in the(2+1)-dimensional Hirota-Satsuma-Ito equation via...Fusion and fission are two important phenomena that have been experimentally observed in many real physical models.In this paper,we investigate the two phenomena in the(2+1)-dimensional Hirota-Satsuma-Ito equation via the physics-informed neural networks(PINN)method.By choosing suitable physically constrained initial boundary conditions,the data-driven fusion and fission solutions are obtained for the first time.Dynamical behaviors and error analysis of these solutions are investigated via illustratively numerical figures,which show that good results are achieved.It is pointed out that the PINN method adopted here can be effectively used to construct the data-driven fusion and fission solutions for other nonlinear integrable equations.Based on the powerful predictive capability of the PINN method and wide applications of fusion and fission in many physical areas,it is hoped that the data-driven solutions obtained here will be helpful for experts to predict or explain related physical phenomena.展开更多
The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbo...The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbolic computation technique.By incorporating a direct variable trans-formation and utilizing Hirota’s bilinear form,multiple rogue wave structures of different orders are ob-tained for both generalized HSI and JM equation.The obtained bilinear forms of the proposed equations successfully investigate the 1st,2nd and 3rd-order rogue waves.The constructed solutions are verified by inserting them into original equations.The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves.Physical properties of these waves are governed by different parameters that are discussed in details.展开更多
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.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11505090)Research Award Foundation for Outstanding Young Scientists of Shandong Province(Grant No.BS2015SF009)+2 种基金the Doctoral Foundation of Liaocheng University(Grant No.318051413)Liaocheng University Level Science and Technology Research Fund(Grant No.318012018)Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology(Grant No.319462208).
文摘This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.
基金supported by the National Natural Science Foundation of China under grant Nos.12371250 and 12205154Jiangsu Provincial Natural Science Foundation under grant Nos.BK20221508 and BK20210380Jiangsu Qinglan High-level Talent Project and High-level Personnel Project under grant No.JSSCBS20210277.
文摘Fusion and fission are two important phenomena that have been experimentally observed in many real physical models.In this paper,we investigate the two phenomena in the(2+1)-dimensional Hirota-Satsuma-Ito equation via the physics-informed neural networks(PINN)method.By choosing suitable physically constrained initial boundary conditions,the data-driven fusion and fission solutions are obtained for the first time.Dynamical behaviors and error analysis of these solutions are investigated via illustratively numerical figures,which show that good results are achieved.It is pointed out that the PINN method adopted here can be effectively used to construct the data-driven fusion and fission solutions for other nonlinear integrable equations.Based on the powerful predictive capability of the PINN method and wide applications of fusion and fission in many physical areas,it is hoped that the data-driven solutions obtained here will be helpful for experts to predict or explain related physical phenomena.
文摘The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbolic computation technique.By incorporating a direct variable trans-formation and utilizing Hirota’s bilinear form,multiple rogue wave structures of different orders are ob-tained for both generalized HSI and JM equation.The obtained bilinear forms of the proposed equations successfully investigate the 1st,2nd and 3rd-order rogue waves.The constructed solutions are verified by inserting them into original equations.The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves.Physical properties of these waves are governed by different parameters that are discussed in details.
