A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrödinger's Equation with Kerr Law Nonlinearity

Abstract

In this paper, we investigate nonlinear the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y. Zhang, et al., Appl. Math. Comput. 216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM), Cosine-function method (CFM). We show that the solutions by using ISM and CFM are equal. Finally, we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).

Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation

“…The reliability of the sub-equation method to solve FPDEs has been demonstrated by applying this method to the space-time fractional Hirota-Satsuma coupled KdV equation. For the special case α=1 and σ=-1, we have successfully recovered the previously known solutions, equations ( 24) and (26), that have been found in Ref. [41].…”

“…wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity [26][27][28][29][30]. Several important aspects of FPDEs have been investigated in recent years; such as the existence and uniqueness of solutions to Cauchy type problems, the methods for explicit and numerical solutions, and the stability of solutions [31,32].…”

New exact traveling wave solutions to the (1+1)-dimensional Klein-Gordon-Zakharov equation for wave propagation in plasma using the exp(-Φ(ξ))-expansion method

“…In particular, the traveling wave solutions play a very important role in the study of these physical models arising from various natural phenomena for the field of applied sciences and engineering. Researchers have used diverse methods to get solutions of nonlinear PDEs, such as, inverse scattering transform [1], the Hirota's bilinear method [2], the tanh method [3], the extended tanh-method [4,5], the modified extended tanh-function method [6,7], the Jacobi elliptic function expansion method [8], the expfunction method [9,10], the improved F-expansion method [11], the exp(-Φ(ξ))-expansion method [12,13], the ðG 0 =GÞ-expansion method [14][15][16][17], the trigonometric function series method [18,19], the modified mapping and extended mapping method [20], the modified trigonometric function series method [21,22], the dynamical system approach [23][24][25], the multiple exp-function method [26], the transformed rational function method [27], the symmetry algebra method (consisting of Lie point symmetries) [28], the Wronskian technique [29], the homogeneous balance method [30], the infinite series and Jacobi elliptic function method [31][32], the first integral method [33], the auxiliary ordinary differential equation method [34] and so on.…”

Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

“…Some other optical waves have been found in many equations. [12][13][14][15][16][17][18][19][20][21] As is well known, the fiber-optic signal plays an important role in real life. It seems that the signal propagation cannot exist in a pure environment.…”