The exact solutions of conformable time-fractional modified nonlinear Schrödinger equation by Direct algebraic method and Sine-Gordon expansion method

Abstract

<abstract><p>In this article, we used direct algebraic method (DAM) and sine-Gordon expansion method (SGEM), to find the analytical solutions of conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE) and finally, we present numerical results in tables and charts.</p></abstract>

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

“…Researchers have focused on finding the analytical or exact solutions to problems which contributes to the analysis of the actual system characteristics. A number of years ago, different efficient and significant methods were developed to obtain solutions, including: the trial equation method, the modified trial equation method [1], the direct algebraic method, the Sine-Gordon expansion method [2], the first integral method, the functional variable method [3], the rational (G ′ /G 2 )-expansion method [4,5], the Nucci's reduction method, the extended hyperbolic method [6], the generalized invariant subspace method [7], the new Kudryashov approach [8], and many others [9][10][11][12][13][14][15].…”

Soliton Solution of the Nonlinear Time Fractional Equations: Comprehensive Methods to Solve Physical Models

“…The study of nonlinear physical models relies on the analysis of wave solutions for nonlinear equations. Recently, numerous and varied methods have been applied to solve NPDEs, such as the Trial equation method [1], functional variable method [2], Sine-Gordon expansion method [3], first integral method [4], and so on [5][6][7][8][9][10][11][12].…”