Abundant invariant and classical solutions with the conservation laws of a new (3+1)-dimensional fifth-order nonlinear Wazwaz equation with the third-order dispersion terms in ocean physics

Abstract

Ocean plays key roles in the earth's system in shaping the planet's climate as well as weather by absorbing, storing, and also transporting huge quantities of carbon-dioxide, water, heat and moisture. This paper presents the analytical examination of a new (3+1)-dimensional fifth-order nonlinear Wazwaz equation with third-order dispersion terms which is applicable in ocean physics and other nonlinear sciences. Ocean physics is the study of various conditions as well as processes that are physical within the ocean, especially the physical features and motions of ocean waters. Thus, the diverse outcomes of the investigations carried out on the model under study possesses significant applications in physical oceanography (Adeyemo, 2022). We first apply Lie group analysis to obtain various infinitesimal generators admitted by the equation. This is followed by invoking the generators to reduce the understudy equation for the purpose of achieving copious group-invariant solutions. We solve the resultant ordinary differential equations in order to obtain diverse classical solutions of the underlying equation. The outcome yields several solutions with arbitrary functions, quadratures, rational and hyperbolic functions alongside various topological kink solitons. Moreover, numerical simulations of the obtained results are performed so as to give some physical interpretations to the solutions and these yield various solitary waves as well as interactions between soliton waves of interest. Furthermore, we outline the applications of our results in ocean physics. Conclusively, conservation laws are constructed for the equation understudy with the use of Ibragimov's theorem.