Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine–cosine method

Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

“…When a NLEE is analysed, one of the most important question is the construction of the exact solutions for equation [1]. In the open literature, quite a few methods for obtaining explicit travelling and solitary wave solutions to NLEEs have been suggested such as the inverse scattering method [2], the bilinear transformation method [3], the tanh-sech method [4,5], the extended tanh method [6,7], the sine-cosine method [8][9][10], the homogeneous balance method [11,12], the pseudo spectral method [13], the G ′ /G -expansion method [14][15][16], exp-function method [17], variational iteration method [18], homotopy perturbation method [19], the Jacobi elliptic function method [20], Lie group analysis method [21] and so on.…”

The Generalized of 𝐜𝐨𝐬𝐡(𝛏) Expansion Method And ItsApplication To Derivative Schrödinger Equation

“…Among these methods are the expansion method [3], the − expansion method [4,5], the generalized of − expansion method [6,7], the Jacobi elliptic function expansion method [8], the generalized Riccati equation method [9,10] the Sine-Cosine Method [11], the −expansion method [12], and various other methods [13][14][15][16].…”

Travelling wave solutions of nonlinear systems of PDEs by using the functional variable method

“…Thus, it is important to investigate the exact explicit solutions of nonlinear systems of partial differential equations. In recent years, various powerful methods have been presented for finding exact solutions of the nonlinear systems of partial differential equations in mathematical physics, such as modified simple equation method [1], Algebraic method [2], sine-cosine method [3], F-expansion method [4], generalized hyperbolic function [5] and functional variable method [6]. Among these methods, the functional variable method is a powerful mathematical tool to solve nonlinear systems of partial differential equations.…”