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
In this paper,we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili(eBKP)equation utilizing the condensed Hirota's approach.In accordance with a logarithmic derivative transform,we produce solutions for si...In this paper,we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili(eBKP)equation utilizing the condensed Hirota's approach.In accordance with a logarithmic derivative transform,we produce solutions for single,double,and triple M-lump waves.Additionally,we investigate the interaction solutions of a single M-lump with a single soliton,a single M-lump with a double soliton,and a double M-lump with a single soliton.Furthermore,we create sophisticated single,double,and triple complex soliton wave solutions.The extended Bogoyavlenskii-Kadomtsev-Petviashvili equation describes nonlinear wave phenomena in fluid mechanics,plasma,and shallow water theory.By selecting appropriate values for the related free parameters we also create three-dimensional surfaces and associated counter plots to simulate the dynamical characteristics of the solutions offered.展开更多
Based on the Hirota’s bilinear form and symbolic computation,the Kadomtsev-Petviashvili equation with variable coefficients is investigated.The lump solutions and interaction solutions between lump solution and a pai...Based on the Hirota’s bilinear form and symbolic computation,the Kadomtsev-Petviashvili equation with variable coefficients is investigated.The lump solutions and interaction solutions between lump solution and a pair of resonance stripe solitons are presented.Their dynamical behaviors are described by some three-dimensional plots and corresponding contour plots.展开更多
According to the N-soliton solution derived from Hirota's bilinear method,higher-order smooth positons and breather positons are obtained efficiently through an ingenious limit approach.This paper takes the Sine-G...According to the N-soliton solution derived from Hirota's bilinear method,higher-order smooth positons and breather positons are obtained efficiently through an ingenious limit approach.This paper takes the Sine-Gordon equation as an example to introduce how to utilize this technique to generate these higher-order smooth positons and breather positons in detail.The dynamical behaviors of smooth positons and breather positons are presented by some figures.During the procedure of deduction,the approach mentioned has the strengths of concision and celerity.In terms of feasibility and practicability,this approach can be exploited widely to study higherorder smooth positons and breather positons of other integrable systems.展开更多
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.
文摘In this paper,we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili(eBKP)equation utilizing the condensed Hirota's approach.In accordance with a logarithmic derivative transform,we produce solutions for single,double,and triple M-lump waves.Additionally,we investigate the interaction solutions of a single M-lump with a single soliton,a single M-lump with a double soliton,and a double M-lump with a single soliton.Furthermore,we create sophisticated single,double,and triple complex soliton wave solutions.The extended Bogoyavlenskii-Kadomtsev-Petviashvili equation describes nonlinear wave phenomena in fluid mechanics,plasma,and shallow water theory.By selecting appropriate values for the related free parameters we also create three-dimensional surfaces and associated counter plots to simulate the dynamical characteristics of the solutions offered.
基金Supported by National Natural Science Foundation of China under Grant No.81860771
文摘Based on the Hirota’s bilinear form and symbolic computation,the Kadomtsev-Petviashvili equation with variable coefficients is investigated.The lump solutions and interaction solutions between lump solution and a pair of resonance stripe solitons are presented.Their dynamical behaviors are described by some three-dimensional plots and corresponding contour plots.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175111 and 11975131K C Wong Magna Fund in Ningbo University。
文摘According to the N-soliton solution derived from Hirota's bilinear method,higher-order smooth positons and breather positons are obtained efficiently through an ingenious limit approach.This paper takes the Sine-Gordon equation as an example to introduce how to utilize this technique to generate these higher-order smooth positons and breather positons in detail.The dynamical behaviors of smooth positons and breather positons are presented by some figures.During the procedure of deduction,the approach mentioned has the strengths of concision and celerity.In terms of feasibility and practicability,this approach can be exploited widely to study higherorder smooth positons and breather positons of other integrable systems.
