On novel resonant multi-soliton and wave solutions to the (3+1)-dimensional GSWE equation via three effective approaches
Chun-Ku Kuo, Behzad Ghanbari
Abstract
In this paper, the generalized shallow water equation (GSWE) is carefully investigated via three state-of-the-art integration schemes, namely the simplified linear superposition principle, velocity resonance, and the trial function method, respectively. The main aim of this work is twofold. The first one is to check the existence of the resonant multi-soliton solutions to GSWE. The second one is to show the power of the trial function method. The simplified linear superposition principle is used to reveal the fact that there have no resonant multi-soliton solutions to GSWE, which is simultaneously confirmed by the velocity resonance. Then, the trial function method is successfully used to obtain new wave solutions. All the newly found solutions are constructed with their existence criteria, and some of them are represented in 3D figures.