Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Abstract

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM. Also, numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement. Besides, the instability modulation of the governing equations are explored through the linear stability analysis function. All new solutions satisfy the main coupled equation after they have been put into the governing equations.

New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

“…Here, the MATLAB symbolic package has been used to illustrate the achieved solutions using the 3D and 2D plotting displays. It can be seen that so many solutions have been derived from newly proposed extended schemes [28,40,41]. We have selected some of the obtained solutions and plotted their physical structures and patterns.…”

Investigation of Analytical Solutions of the Nonlinear Mathematical Model Representing Gas Overflowing

“…Considering the balancing procedure for Eqn. (12), the following equation is obtained regarding the upper limits of the symbols of the sum in Eqn.…”

“…For this reason, there are various methods or techniques in the literature about establishing such mathematical models and analyzing their solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

“…More general properties of auxiliary and sub-equation function methods have been comprehensively introduced in the literature [28,29]. Moreover, there are many published methods for solving similar equations using different techniques and methods [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”