Approximate Simulations for the Non-linear Long-Short Wave Interaction System

Abstract

This research paper studies the semi-analytical and numerical solutions of the non-linear long-short wave interaction system. This represents an optical field that does not change through multiplication due to a sensitive balance being struck between linear and non-linear impacts in an elastic medium, defined as a medium that can adjust its shape as a consequence of deforming stress and return to its original form when the force is eliminated. In this medium, a wave is produced by vibrations that are a consequence of acoustic power, known as a sound wave or acoustic wave. The Adomian decomposition method and the cubic and septic B-spline methods are applied to the suggested system to obtain distinct types of solutions that are used to explain the novel physical properties of this system. These novel features are described by different types of figures that show more of the physical properties of this model. Also, the convergence between the obtained solutions is discussed through tables that show the values of absolute error between them.

Abundant Wave Accurate Analytical Solutions of the Fractional Nonlinear Hirota–Satsuma–Shallow Water Wave Equation

“…Such techniques are used to construct the analytical solutions for example extended tanh-expansion method, rational-expansion method, sine-Gordon expansion method, inverse Scattering transformation, Darbous transformation, Riccati, expansion method, multiple exp-function method, etc. [13,[15][16][17][18][19][20][21][22][23][24][25][26].…”

Computational solutions of the HIV-1 infection of CD4+T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy

“…The other sections of this paper are organized, as follows: Section 2 applies the septic B-spline scheme [32] , [50] based on the obtained analytical solutions via the modified Khater, extended simplest equation, and sech-tanh expansion methods to the fractional ODE model of the HIV-1 infection of CD4 T–cells to study the numerical solutions via various explicit solutions. Moreover, some sketches of the exact and numerical solutions of the system are presented to illustrate the accuracy of our obtained solutions.…”

Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells

“…These works have been deriving many analytical and numerical mathematical schemes to construct analytical, semi-analytical, approximate solutions. These schemes are based on three mainly channels, namely Lie group techniques, reduction techniques and ansatz techniques [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”