Soliton Solutions of the Nonlinear Time Fractional Harry Dym Equation in the Caputo Sense and the Symmetric Regularized Long Wave Equation in the Conformable Sense

Abstract

In this paper, we apply two different methods, namely, the G G-expansion method and G G 2-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equation in the conformable sense. The mentioned NPDES arise in diverse physical applications like ion sound waves in plasma and waves on shallow water surfaces. There exist multiple wave solutions to many NPDEs and one is interested in analytical approaches for obtaining multiple wave solutions to NPDEs. The multi-exp-function method formulates a solution algorithm for calculating multiple wave solutions to NPDEs and at the end of paper, we apply the MEFM for calculating multiple wave solutions to the (2+1)-dimensional equation.

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].…”