Based on a transformed Painleve property and the variable separated ODE method, a function transformationmethod is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic o...Based on a transformed Painleve property and the variable separated ODE method, a function transformationmethod is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic orexponential functions.This approach provides a more systematical and convenient handling of the solution process of thiskind of nonlinear equations.Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleveproperty and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions tothe resulting equations by some methods.As an application, exact solutions for the combined sinh-cosh-Gordon equationare formally derived.展开更多
In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh m...In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh methods are used.In addition,an extension of the recent polynomial function method is applied as well.Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs.Finally,some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.展开更多
The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation ha...The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation has a hypothetical soliton solutions.By reorganizing the resulting equations,we obtain a system of equations.Using Maple software,we get unknown coefficients in the system and writing them in the original equation,we obtain new solition solutions of the equation.The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright,kink type,bright periodic and dark solutions.We provided 3-D figures to illustrate the solutions.Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10926057 Foundation of Zhejiang Educational Committee under Grant No.Y200908784
文摘Based on a transformed Painleve property and the variable separated ODE method, a function transformationmethod is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic orexponential functions.This approach provides a more systematical and convenient handling of the solution process of thiskind of nonlinear equations.Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleveproperty and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions tothe resulting equations by some methods.As an application, exact solutions for the combined sinh-cosh-Gordon equationare formally derived.
文摘In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh methods are used.In addition,an extension of the recent polynomial function method is applied as well.Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs.Finally,some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.
文摘The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation has a hypothetical soliton solutions.By reorganizing the resulting equations,we obtain a system of equations.Using Maple software,we get unknown coefficients in the system and writing them in the original equation,we obtain new solition solutions of the equation.The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright,kink type,bright periodic and dark solutions.We provided 3-D figures to illustrate the solutions.Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.
