Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique
Villévo Adanhounme *
International Chair in Mathematical Physics and Applications (ICMPA), University of Abomey-Calavi, 01 PO Box 526 Cotonou, Benin.
Gaston Edah
International Chair in Mathematical Physics and Applications (ICMPA), University of Abomey-Calavi, 01 PO Box 526 Cotonou, Benin and Department of Physics, Faculty of Sciences and Technology (FAST), University of Abomey-Calavi, Benin.
Norbert M. Hounkonnou
International Chair in Mathematical Physics and Applications (ICMPA), University of Abomey-Calavi, 01 PO Box 526 Cotonou, Benin and Department of Physics, Faculty of Sciences and Technology (FAST), University of Abomey-Calavi, Benin.
*Author to whom correspondence should be addressed.
Abstract
We study the higher-order nonlinear Schrödinger equation which takes care of the second as well as third order dispersion effects, cubic and quintic self phase modulations, self steepening and nonlinear dispersion effects. Taking advantage of the initial condition, we transform the
previous equation into a nonlinear functional equation to which we apply a powerful analytical method called the Adomian decomposition method. We compute the Adomian’s polynomials of corresponding infinite series solution. Assuming that the initial condition and all its derivatives converge to zero sufficiently rapidly as the time approaches to infinity, we established the convergence of the previous series. The last part of the paper describes applications resulting from nonlinear propagation phenomena in optical fibers. Numerical simulations are developed and it is further shown that comparison with other results yields a good qualitative agreement. These results demonstrate the robustness of the proposed method.
Keywords: Higher-order nonlinear Schrödinger equation, Adomian decomposition technique, optical fibers