The Classification of all Single Traveling Wave Solutions to Fornberg-Whitham Equation
نویسندگان
چکیده
Under the traveling wave transformation, Fornberg-Whitham equation is reduced to an ordinary differential equation whose general solution can be obtained using the factorization technique. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtain the classification of all single traveling wave solutions to the Fornberg-Whitham equation.
منابع مشابه
Periodic and Solitary Wave Solutions to the Fornberg-Whitham Equation
In this paper, new travelling wave solutions to the Fornberg-Whitham equation ut − uxxt + ux + uux = uuxxx + 3uxuxx are investigated. They are characterized by two parameters. The expresssions of the periodic and solitary wave solutions are obtained.
متن کاملModified F-Expansion Method Applied to Coupled System of Equation
A modified F-expansion method to find the exact traveling wave solutions of two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...
متن کاملSolitons, peakons and periodic cusp wave solutions for the Fornberg-Whitham equation
In this paper, we employ the bifurcation method of dynamical systems to investigate the exact travelling wave solutions for the Fornberg-Whitham equation ut − uxxt + ux+uux = uuxxx+3uxuxx. The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp ...
متن کاملA type of bounded traveling wave solutions for the Fornberg-Whitham equation
In this paper, by using bifurcation method, we successfully find the FornbergWhitham equation ut − uxxt + ux = uuxxx − uux + 3uxuxx, has a type of traveling wave solutions called kink-like wave solutions and antikinklike wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some c...
متن کاملSolving Fractional Fornberg-whitham Equation by Homotopy Analysis Method
In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...
متن کامل