Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

Abstract

This research paper explores the Atangana conformable nonlinear fractional Schrödinger equation’s optical soliton wave solutions through three recently introduced computational schemes. The simplest expanded equation, the generalized Kudryashov method, and the sech-tanh expansion approaches are used for describing the structure of optical solitons by nonlinear optical fibers with the modern fractional operator. Several formulas such as hyperbolic, trigonometric, logical, dim, light, moon-bright hybrid, singular, combined singular, and regular wave solutions have been created. The employed methods are effective and worthy of being tested. The features of the Hamiltonian process were used to analyze the stability properties of the solutions obtained.

Collisional Solitons Described by Two-Sided Beta Time Fractional Korteweg-de Vries Equations in Fluid-Filled Elastic Tubes

“…It is noted that many authors [26][27][28][29][30][31] have studied the wave phenomena by considering the fractional evolution equations. They have ignored how to form such equations from the evolution equations of integer orders.…”

Some traveling wave solutions to the generalized (3 + 1)‐dimensional Korteweg–de Vries–Zakharov–Kuznetsov equation in plasma physics

“…For precisely generating traveling wave solutions, solitary wave solutions, and the dynamics of these solutions to such models, a number of analytical and numerical methodologies have recently been devised. The Jacobi elliptic function expansion technique, 7,8 the Hirota bilinear technique, 9 the generalized unified technique, 10,11 the tanh-coth expansion technique, 12,13 the sub ODE technique, 14,15 the extended Sinh-Gordon equation technique, [16][17][18][19] the first integral technique, [20][21][22] the extended simplest equation technique, [23][24][25][26] generalized exponential rational function method, 27 modified khater method, 28,29 new Kudryashov technique, [30][31][32] modified direct algebraic technique, [33][34][35] generalized auxiliary equation technique, 36 generalized Riccati equation technique, 37,38 the modified simple equation technique, [39][40][41] Lie symmetry technique, [42][43][44] the extended Tanh technique, 45,46 the 𝜙 6 -expansion technique, 47 and the Homogeneous balance method, …”