Construction of soliton solutions for modified Kawahara equation arising in shallow water waves using novel techniques

Abstract

The modified Kawahara equation also called Korteweg-de Vries (KdV) equation of fifth-order arises in shallow water wave and capillary gravity water waves. This study is based on the generalized Riccati equation mapping and modified the F-expansion methods. Several types of solitons such as Bright soliton, Dark-lump soliton, combined bright dark solitary waves, have been derived for the modified Kawahara equation. The obtained solutions have significant applications in applied physics and engineering. Moreover, stability of the problem is presented after being examined through linear stability analysis that justify that all solutions are stable. We also present some solution graphically in 3D and 2D that gives easy understanding about physical explanation of the modified Kawahara equation. The calculated work and achieved outcomes depict the power of the present methods. Furthermore, we can solve various other nonlinear problems with the help of simple and effective techniques.