Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method

Abstract

In this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schrödinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some illustrative examples are presented to show the validity of the proposed technique without using any polynomials. The proposed method provides the series form solutions, which converge to the exact results. Using the present methodology, the solutions of fractional-order problems as well as integral-order problems are calculated. The present method has less computational costs and a higher rate of convergence. Therefore, the suggested algorithm is constructive to solve other fractional-order linear and nonlinear partial differential equations.

Nonlocal Fractional Hybrid Boundary Value Problems Involving Mixed Fractional Derivatives and Integrals via a Generalization of Darbo’s Theorem

“…For some recent results for boundary value problems involving left or/and right fractional derivatives, we refer to the papers [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and references therein.…”

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

“…These transforms provided in the literature are applied to solve several integral equations, ODEs, PDEs, and fractional PDEs [10][11][12][13][14][15][16][17]. Fusion of these transforms with semi-analytical techniques such as ADM, DTM, HPM, and VIM can also create novel and efficient regimes to solve such equations [18][19][20][21][22][23][24][25][26][27]. A coupled non-linear Schrodinger-KdV and Maccari system is solved using q-HATM [28,29].…”

A Semi-Analytical Method to Investigate Fractional-Order Gas Dynamics Equations by Shehu Transform

“…The differential transformation approach [7] was utilized to solve the homogeneous and nonhomogeneous nonlinear gas dynamics equations. Some methods have been investigated by gas dynamics equations, such as the homotopy perturbation transformation method [8], fractional reduced differential transform method [9], Adomian decomposition method [10], q-homotopy analysis method [11], fractional homotopy analysis transformation method [12], variational iteration method [13,14], homotopy perturbation method applying Laplace transformation [15], and natural decomposition method [16].…”