Computational simulations of propagation of a tsunami wave across the ocean

Abstract

The 2D regularized long-wave equation is a mathematical model used to describe the behavior of water waves in two dimensions, taking into account nonlinear and dispersive effects. To obtain soliton wave solutions, computational methods have been employed to solve this equation. Solitons are localized wave solutions that maintain their shape and speed over long distances, making them useful in various applications, such as optical fiber communication and modeling water waves. This study utilized the Khater II, septic-B-spline, and Adomian decomposition techniques to solve the 2D regularized long-wave equation and obtain soliton wave solutions. The results showed a wide range of soliton solutions, including bright and dark solitons as well as soliton pairs and chains. Furthermore, we investigated the impact of the regularization parameter on the soliton solutions and observed that it affects the soliton speed and shape. Our findings demonstrate how computers can be utilized to obtain new soliton wave solutions for the 2D regularized long-wave equation, which have implications for various fields, such as oceanography, engineering, and physics. By understanding how solitons behave within the context of this equation, we can create more accurate models of water waves and other physical systems.