Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

Abstract

We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G /G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before.

Exact solutions and linear stability analysis for two-dimensional Ablowitz–Ladik equation

“…[24], Maruno et al derived a set of exact solutions which includes, as particular cases, bright and dark soliton solutions, constant magnitude solutions with phase shifts, periodic solutions in terms of elliptic Jacobi functions in general forms, and various particular periodic solutions to discrete complex cubic-quintic Ginzburg-Landau equation with a non-local quintic term. Aslan, etc used the -expansion method to derive the discrete solitons of the discrete nonlinear Schrodinger-type equations [25][26] . In the practical application, only stable soliton is valuable.…”

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

“…Zhang et al [21] have modified the ( / ) expansion method form solving the nonlinear partial differential equations to solve the nonlinear differential difference equations. Aslan [22,23] has applied the ( / ) expansion method for solving the discrete nonlinear Schrodinger equations with a saturable nonlinearity, discrete Burgers equation, and the relativistic Toda lattice system. More recently Gepreel et al [24][25][26] have used the modified rational Jacobi elliptic functions method to construct some types of Jacobi elliptic solutions of the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, and the quintic discrete nonlinear Schrodinger equation.…”

Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method

“…In the literature, many of these methods among which we find are: the Hirotas bilinear method [19], the Backlund transformation method [20], the Darboux transformation method [21], the Painleve singularity structure analysis method [22], the Riccati expansion with constant coefficients [23], the variational iteration method [24], the exp-function method [25], the algebraic method [26], the collocation method [27], the Kudryashov method [28][29][30][31][32], the (G /G)-expansion method [33][34][35][36][37][38], the simplest equation method [39][40][41][42][43], and so on. However, some of these analytical methods are not easy to handle and are often subject to tedious mathematical developments.…”