A study on two coupled modified KdV systems with time-dependent and constant coefficients
نویسندگان
چکیده
This work concerns itself on two new coupled mKdV systems, the first with time-dependent coefficients, and the second with constant coefficients. The soliton ansatz will be used for the first system to obtain 1-bright soliton solution. The simplified form of the bilinear method will be used to derive multiple-soliton solutions and multiple singular soliton solutions for the second coupled mKdV system.
منابع مشابه
Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملDYNAMIC BEHAVIOR OF TRAVELING WAVE SOLUTIONS FOR A CLASS FOR THE TIME-SPACE COUPLED FRACTIONAL kdV SYSTEM WITH TIME-DEPENDENT COEFFICIENTS
In this paper, a simplified bilinear method combined with a fractional transform has been used to obtain a new multiple soliton solutions for the Fractional coupled fractional kdV equations with variable coefficients. These systems appear in biology, engineering, mechanics, complex physics phenomena economics, signal image processing, notably control theory, groundwater problems and chemistry. ...
متن کاملSolution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...
متن کاملOn shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV e...
متن کاملThree-dimensional analytical models for time-dependent coefficients through uniform and varying plane input source in semi-infinite adsorbing porous media.
In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...
متن کامل