Periodic and solitary wave solutions of some important physical models with variable coefficients

Abstract

ABSTRACT In this paper, we construct the family of traveling wave solutions for various kinds of nonlinear integral and fractional order evolution equations with variable coefficients. Specifically, we consider the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and (1+1)-dimensional Benney-Luke equation as integeral order partial differential equations and the combined KdV-mKdV equation with time-dependent coefficients as fractional order partial differential equation. More precisely, the improved system technique has been implemented to obtain traveling wave solutions of the considered nonlinear evolution equations with variable coefficients. Further, the integrability of the combined fractional order KdV-mKdV equation with time-dependent coefficients is tested via Painlevé test. As a result, several exact traveling wave solutions have been successfully derived and subsequently their dynamical behaviors are visualized through graphically. The result reveals that the improved system technique is an effective and useful tool to obtain exact traveling wave solutions of both integral and fractional order nonlinear evolution equations with variable coefficients arising in various physical problems.