Optical Solitons with Time-Dependent Dispersion, Nonlinearity and Attenuation in a Kerr-Law Media

Abstract

This paper obtains the 1-soliton solution of the nonlinear Schrödinger's equation with Kerr law nonlinearity and time-dependent dispersion, nonlinearity and attenuation. The solitary wave ansatze is used to obtain this solution. The constraint relation between these time-dependent coefficients is also obtained for the solitons to exist. The variation of the soliton velocity also falls out by this method.

NEW (F/G )-EXPANSION METHOD AND ITS APPLICATIONS TO NONLINEAR PDES IN MATHEMATICAL PHYSICS Vol. 4(1) Jan. 2016, No. 17, pp. 175-183 M. MORTAZAVI, M. GACHPAZAN

“…Today there are several and ever in creasing number of papers that are being published in this area of research ([1]- [30]). The solutions of nonlinear equations play a crucial role in applied mathematics and physics, because; solutions of nonlinear partial differential equations provide a very significant contribution to people about the exact solutions of nonlinear evolution equations have been established and developed, such as the tanh-coth function expansion ( [1]- [4]), the solitary wave ansatz method ( [5]- [8]), Lie symmetry analysis [9], the sub-ODE method [10], exp-function method [11,12], the homogeneous balance method [13], the first integral method [14,15], the simplest equation method [16,17] and so on. But there is no unified method that can be used to deal with all types of nonlinear avolution equations.…”

Solitary wave solutions for perturbed nonlinear Schrodinger's equation with Kerr law nonlinearity under the DAM

“…Recently many new approaches for finding the exact solutions to nonlinear wave equations have been proposed, such as, direct algebraic method [1], simplest equation method [2,3], tanh method [4,5], multiple exp-function method [6], Backlund transformation method [7], Hirotas direct method [8,9], transformed rational function method [10], and so on [11][12][13][14][15][16].…”

Binary simplest equation method to the generalized Sinh–Gordon equation

“…To this aim, a vast variety of powerful and direct methods for finding the exact significant solutions of NLPDEs though it is rather difficult have been derived. Some of the most important methods are tanhextended tanh method [6][7][8], solitary wave ansatze method [9][10][11], tanh method [12,13], multiple expfunction method [14], Kudryashov method [15][16], Hirota's direct method [17,18], transformed rational function method [19] and others [20]. They produce many kinds of exact solutions to a given evolution equations.…”