Analysis of travelling wave solutions of double dispersive sharma-Tasso-Olver equation

Abstract

Travelling wave solutions have been played a vital role in demonstrating the wave character of nonlinear problems arising in the field of ocean engineering and sciences. To describe the propagation of the nonlinear wave phenomenon in the ocean (for example, wind waves, tsunami waves), a variety of evolution equations have been suggested and investigated in the existing literature. This paper studies the dynamic of travelling periodic and solitary wave behavior of a double–dispersive non-linear evolution equation, named the Sharma-Tasso-Olver (STO) equation. Nonlinear evolution equations with double dispersion enable us to describe nonlinear wave propagation in the ocean, hyperplastic rods and other mediums in the field of science and engineering. We analyze the wave solutions of this model using a combination of numerical simulations and Ansatz techniques. Our analysis shows that the travelling wave solutions involve a range of parameters that displays important and very interesting properties of the wave phenomena. The relevance of the parameters in the travelling wave solutions is also discussed. By simulating numerically, we demonstrate how parameters in the solutions influence the phase speed as well as the travelling and solitary waves. Furthermore, we discuss instantaneous streamline patterns among the obtained solutions to explore the local direction of the components of the obtained solitary wave solutions at each point in the coordinate (x,t).