Novel anlytical solution to the damped Kawahara equation and its application for modeling the dissipative nonlinear structures in a fluid medium

Abstract

A novel approximate analytical solution to the linear damped Kawahara equation using a suitable hypothesis is reported for the first time. Based on the exact solutions (such as solitary waves, cnoidal waves, etc.) of the undamped Kawahara equation, the dissipative nonlinear structures like dissipative solitons and cnoidal waves are investigated. The obtained solution is considered a general solution, i.e., it can be applied for studying the properties of all dissipative traveling waves described by the linear damped Kawahara equation. Our technique is not limited to solve the linear damped Kawahara equation only, but it can be used for solving a large number of non-integrable evolution equations related to the realistic natural phenomena. Moreover, the maximum global residual error in the whole space-time domain is estimated for checking the accuracy of the obtained solutions. The obtained solutions can help many researchers in explaining the ambiguities about the mechanisms of propagation of nonlinear waves in complex systems such as seas, oceans, plasma physics, and much more.