A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant speed.Solitons are caused by the cancellation of the medium’s nonlinear and dispersive effects.In plas-mas,the bi...A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant speed.Solitons are caused by the cancellation of the medium’s nonlinear and dispersive effects.In plas-mas,the bilinear form of Hirota will be utilized to investigate the(2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential.Solutions for complexiton lump interaction have been devel-oped.To throw further light on the physical qualities of the recorded data,certain 3-dimensional and contour plots are presented to illustrate the interaction elements of these solutions.展开更多
The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,co...The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves.In this paper,this equation is investigated and analyzed using two effective schemes.The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration.The breather wave solutions are derived using the Cole–Hopf transformation.In addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund symmetries.The novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.展开更多
1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact ...1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.展开更多
文摘A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant speed.Solitons are caused by the cancellation of the medium’s nonlinear and dispersive effects.In plas-mas,the bilinear form of Hirota will be utilized to investigate the(2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential.Solutions for complexiton lump interaction have been devel-oped.To throw further light on the physical qualities of the recorded data,certain 3-dimensional and contour plots are presented to illustrate the interaction elements of these solutions.
文摘The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves.In this paper,this equation is investigated and analyzed using two effective schemes.The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration.The breather wave solutions are derived using the Cole–Hopf transformation.In addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund symmetries.The novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos. 10831003,61072147,11071159)+2 种基金the Shanghai Municipal Natural Science Foundation (No. 09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)TUBITAK (the Scientific and Technological Research Council of Turkey) for its financial support and grant for the research entitled "Integrable Systems and Soliton Theory" at University of South Florida
文摘1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.
