Dynamics of closed-form invariant solutions and diversity of wave profiles of (2+1)-dimensional Ito integro-differential equation via Lie symmetry analysis

Abstract

Nonlinear evolution equations are exploited in the models of complex nonlinear phenomena, explaining a number of our real-world problems in different fields of engineering and nonlinear sciences, for example, the modeling of interactions between ocean forces and the atmosphere, fiber optics, fluid dynamics, plasma physics, marine physics, and nonlinear dynamics. In this work, a comparatively new Lie symmetry analysis technique has been effectively implemented to explore some closed-form invariant solutions of the (2+1)-dimensional Ito equation. This technique is essential to minimize the number of independent variables by one at each stage until an ordinary differential equation (ODE) is formed. By utilizing the invariance analysis, the possible infinitesimal generators are derived, which are used to reduce the test problem and lead to determining the ODEs. All the exact solutions obtained are totally novel and differ significantly from previously published results. Due to the existence of some different arbitrary constants and functions, the solution provides a wealth of physical configurations. The solutions obtained in this article are thrust into the giant wave solutions such as curved shaped multi-solitons, parabolic waves, solitary waves, and traveling wave profiles displayed using three-dimensional (3D) wave patterns. Finally, we used symbolic computations in Mathematica to verify all the obtained soliton solutions. Furthermore, the current method’s superior expertise ensures that it is essentially capable of reducing the size of the computational assignment and can solve a variety of complex nonlinear partial differential equations (NLPDEs) that arise in many fields of nonlinear sciences, ocean engineering, nonlinear waves, and fluid dynamics.