Multiple Solitons Solutions, Conserved Vectors and Other Solutions of an Extended Fourth-Order Equation for the Shallow Water Waves

Abstract

This work aims to implement solitary wave ansatz methods to carry out the integration of an extended (3+1)-dimensional integrable fourth-order nonlinear equation which occurs in the study of shallow water waves. Other analytical solutions via the symmetry method are also derived. The extended (3+1)-dimensional integrable fourth-order nonlinear equation investigated in this work is more physical meaningful due to the presence of the three dissipative terms. These three terms signify dissipative mechanism in the x-direction, y-direction and z-direction depending on the sign of \(\kappa , \delta \) and \(\sigma \), respectively. The results derived in this work are new and cannot be reachable anywhere in the literature. The conditions under which the solitary solutions exist are outlined. The dynamic performances of the derived solutions are displayed graphically to represent the physical interpretations. Moreover, the multiplier approach will be employed to derive local conserved vectors.