The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Abstract

In this paper, the generalized exponential rational function method (GERFM) and the extended sinh-Gordon equation expansion method (ShGEEM) are used to construct exact solutions of the perturbed β-conformable-time Radhakrishnan-Kundu-Lakshmanan (RKL) equation. This model governs soliton propagation dynamics through a polarization-preserving fiber. Fractional derivatives are described in the β-conformable sense. As a result, we get new form of solitary traveling wave solutions for this model including novel soliton, traveling waves and kink-type solutions with complex structures. Physical interpretations of some extracted solutions are also included through taking suitable values of parameters and derivative order in them. It is proved that these methods are powerful, efficient, and can be fruitfully implemented to establish new solutions of nonlinear conformable-time partial differential equations applied in mathematical physics.

Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques

“…Inserting Eqs. (8)(9)(10)(11) into Eq. (2), followed by uncoupling of real and imaginary parts of the equation gives a pair of equations, i.e., the real part is…”

“…The analysis of such equations provides insightful physical information, useful for further applications. Many trails have been penned for the physical problems in the last years to get the analytical solutions of the NLPDEs with the recent computer technology [1][2][3][4][5][6][7][8][9][10][11][12]. A variety of powerful methods have been developed such as the exp(−φ(ζ))expansion expansion method [13,14], the (G /G)-expansion method [15,16], the new extended direct algebraic method [17,18], the first integral method [19,20], the extended Jacobi elliptic function expansion method [21,22], and so on [23][24][25][26][27][28][29][30].…”

Optical soliton solutions of nonlinear Davey-Stewartson equation using an efficient method

“…The authors applied the technique to solve the resonant nonlinear Schrödinger equation (R-NLSE). It has been proven over time that the method enables us to be implemented in many different NPDEs arising in mathematics, physics, and engineering [45][46][47][48][49][50][51][52][53][54]. The proposed method reproduces many types of precise solutions, and it is very useful for finding the exact solutions of the equation with relative ease.…”

Application of the modified simple equation method for solving two nonlinear time-fractional long water wave equations

“…Therefore, researchers have been doing great efforts to introduce new powerful and effective methods to solve these equations. Among which the modified simple equation (MSE) method [4], the generalized Kudryashov method [5], the (G /G)-expansion method [6], the improved Fexpansion method [7], the generalized exponential rational function method [8], the first integral method [9], the generalized bifurcation method [10], the modified trial equation method [11], the extended auxiliary equation method [12], the conformable double Sumudu transform [13], the conformable sub-equation method [14], the new extended direct algebraic method [15], the generalized (G /G)-expansion method [16], the homotopy perturbation method [17] and collocation methods [18,19] are just a few to name. In the literature, there are several types of fractional derivatives.…”