Analytical and computational approaches on solitary wave solutions of the Generalized Equal Width Equation

Abstract

In this article, firstly numerical solutions of the generalized equal width (GEW) equation have been obtained by a Petrov-Galerkin finite element method using cubic B-spline base functions as element shape functions and quadratic B-spline base functions as the weight functions. In order to prove the practicability and robustness of the numerical algorithm, the error norms L2, L∞ and three invariants I1, I2 and I3 are computed. A linear stability analysis based on a Fourier method states that the numerical scheme is unconditionally stable. Secondly, we have proposed the modified extended tanh-function method with the Riccati differential equation, which is a convenient and an effective method, for getting the exact traveling wave solutions of the equation. Motion of single solitary wave is examined using the present methods. The obtained results are indicated both in tabular and graphical form.