A modified generalized projective Riccati equation method

The Extended Generalized Riccati Equation Mapping Method for the (1+1)-Dimensional Modified KdV Equation

where p,q and r are arbitrary constants. We construct twenty five exact traveling wave solutions of the (1+1)-dimensional modified KdV equation involving parameter by applying this method. The solutions are presented in terms of the hyperbolic, the trigonometric and the rational functional form including solitons and periodic solutions. Moreover, it is worth mentioning that one of our obtained ...

Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

1 Departamento de Matemáticas, Universidad Nacional de Colombia, Calle 45, Carrera 30, P.O. Box: Apartado Aéreo: 52465, Bogotá, Colombia 2 Departamento de Matemáticas, Universidad Nacional de Colombia, Carrera 27 no. 64–60, P.O. Box: Apartado Aéreo 127, Manizales, Colombia 3 Departamento de Matemáticas, Universidad de Caldas, Calle 65 no. 26–10, Caldas, P.O. Box: Apartado Aéreo 275, Manizales, ...

Exact Solutions for Nonlinear Evolution Equations Via Extended Projective Riccati Equation Expansion Method

Abstract: By means of a simple transformation, we have shown that the generalized-Zakharov equations, the coupled nonlinear Klein-Gordon-Zakarov equations, the GDS, DS and GZ equations and generalized Hirota-Satsuma coupled KdV system can be reduced to the ellipticlike equations. Then, the extended projective Riccati equation expansion method is used to obtain a series of solutions including ne...

Exact Solutions for Fractional Partial Differential Equations by Projective Riccati Equation Method

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

Riccati equation, Factorization Method and Shape Invariance