Dynamical behavior of the long waves on the surface of the water with a small amplitude in none–dimensional nonlinear lattices

Abstract

Analytic and approximation solutions to the Ill–posed Boussinesq (IPB) problem are constructed using two modern computational and numerical approaches. In shallow water, this equation represents the propagation of waves under the effect of gravity. It also examines the propagation of nonlinear strings and lattices in one-dimensional nonlinear systems. Additionally, the nonlinear strings and none-dimensional nonlinear lattices have lengthy waves on the surface with modest amplitudes described by the IPB model. The primary aims of our work are to obtain new analytical solutions and utilize those answers to assess beginning and boundary conditions to apply numerical methods to the same problem. In order to determine how accurate a solution is, the absolute value of the error between numerical and analytical results is calculated. Additionally, several diagrams are provided to describe the physical features of these waves in greater detail.