Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation

Abstract

The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique and residual power series method are utilized to build new exact and analytical approximate solutions of the time-fractional potential Korteweg-de Vries equation. The dynamics of the solutions obtained are explored by drawing them in two and three dimensions. Comparisons between the new results and the solutions available in literature show that the presented approaches of nonlinear problem resolution are highly effective and reliable. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena.

Keywords

• Wave solutions
• Modified auxiliary equation method
• Residual power series method
• Caputo fractional derivative
• Jumarie’s modified Riemann-Liouville derivative