Resonant multi-soliton solutions to two fifth-order KdV equations via the simplified linear superposition principle

Abstract

In this paper, the simplified linear superposition principle is presented and employed to handle two versions of the fifth-order KdV equations, called the (2[Formula: see text]+[Formula: see text]1)-dimensional Caudrey–Dodd–Gibbon (CDG) equation and the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation, respectively. Two general forms of resonant multi-soliton solutions are formally obtained. The paper proceeds step-by-step with increasing detail about the derivation process. Firstly, illustrate the algorithms of the linear superposition principle which paves the way for solving the wave related numbers. Then, demonstrate its application that exposes the proposed approach provides enough freedom to construct resonant multi-soliton wave solutions. Finally, some graphical representations of obtained solutions are portrayed by taking some definite values to free parameters, which describe various versions of inelastic interactions of resonant multi-soliton waves. The associated propagations may be related to large variety of real physical phenomena.