In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

In this paper, the ( / ) G G  -expansion method is extended to solve fractional differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order. For illustrating the validity of this method, we apply it to fi...

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differe...

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave soluti...

By using the integral bifurcation method, we study the nonlinearK m,n equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton...

In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation. Keywords—Exact solution, The (3+1)-dimensiona...

In the paper, a auxiliary equation expansion method and its a lgorithm is proposed by studying a second order nonlinear ordinary differential equation with a six-degree term.The method is applied to the generalized derivative Schrödinger equation .As a result,some new exact traveling wave solution are obtained which singular solutions,triangular periodic wave solution and Jacobian elliptic func...

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved ( ′ G )expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G′(ξ)]2 = aG2(ξ) + bG4(ξ) + cG6(ξ), where ξ = x − V t while a, b, c and V...

In this work, the generalized ( G′ G ) -expansion method is presented to seek some new exact solutions for generalized fifth order KdV equation with time-dependent coefficients. As a result, more explicit traveling wave solutions involving arbitrary parameters are found out, which are expressed in terms of hyperbolic functions, the trigonometric functions and rational functions. When the parame...