Abstract
In this paper, we propose the extended Boussinesq–Whitham–Broer–Kaup (BWBK)-type equations with variable coefficients and fractional order. We consider the fractional BWBK equations, the fractional Whitham–Broer–Kaup (WBK) equations and the fractional Boussinesq equations with variable coefficients by setting proper smooth functions that are derived from the proposed equation. We obtain uniformly coupled fractional traveling wave solutions of the considered equations by employing the improved system method, and subsequently their asymmetric behaviors are visualized graphically. The result shows that the improved system method is effective and powerful to find explicit traveling wave solutions of the fractional nonlinear evolution equations.
Highlights
Nonlinear partial differential equations (NPDEs) play an important role to describe nonlinear physical phenomena that can be described by the solutions of NPDEs rising in physics, biology, chemistry, mechanics and mathematical engineering
The present paper is based on Equation (1), and we propose the extended BWBK-type equations with variable coefficients and fractional order as follows:
We provide a short description of the improved system method with parameter functions for constructing the explicit solutions of the fractional NPDEs
Summary
Nonlinear partial differential equations (NPDEs) play an important role to describe nonlinear physical phenomena that can be described by the solutions of NPDEs rising in physics, biology, chemistry, mechanics and mathematical engineering. Explicit wave solutions of the fractional nonlinear evolution equations have great significance to reveal internal mechanisms of physical phenomena as fractional orders. The present paper is based on Equation (1), and we propose the extended BWBK-type equations with variable coefficients and fractional order as follows:.
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