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
In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable...In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.展开更多
The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equa...The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.展开更多
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.
文摘In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.
文摘The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.
