New exact soliton and periodic wave solutions of the nonlinear fractional evolution equations with additional term

Abstract

This paper presents exact solutions for the fractional Korteweg–de Vries equation and the fractional modified Korteweg–de Vries equation with additional term using the functional variable method. The main advantage of the proposed functional variable method over other methods is that it provides more accurate traveling wave solutions with additional free parameters. As a result, soliton and periodic wave solutions are obtained. It is shown that the calculations in the functional variable method are very simple and easy to understand, and this method is very effective for handling nonlinear fractional equations. Exact solutions are great importance in revealing the internal mechanism of physical phenomena. This method presents a wider applicability for handling nonlinear fractional-order wave equations.

Keywords

• The fractional Korteweg–de Vries equation
• The nonlinear fractional modified Korteweg–de Vries equation
• Periodic wave solutions
• Soliton wave solutions
• Functional variable method
• Additional term