Solving Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique
Gaston Edah *
Département de Physique, Faculté des Sciences et Techniques, Université d’Abomey-Calavi, BP 526 Cotonou, Bénin and International Chair of Mathematical Physics and Applications (ICMPA-Unesco Chair), BP 526 Cotonou, Université d’Abomey-Calavi, Bénin.
Villévo Adanhoumè
International Chair of Mathematical Physics and Applications (ICMPA-Unesco Chair), BP 526 Cotonou, Université d’Abomey-Calavi, Bénin.
Marc Amour Ayela
Institut de Mathématiques et de Sciences Physiques, Université d’Abomey-Calavi, BP 526 Cotonou, Bénin.
*Author to whom correspondence should be addressed.
Abstract
In this paper, using a suitable change of variable and applying the Adomian decomposition method to the generalized nonlinear Schr¨odinger equation, we obtain the analytical solution, taking into account the parameters such as the self-steepening factor, the second-order dispersive parameter, the third-order dispersive parameter and the nonlinear Kerr effect coefficient, for pulses that contain just a few optical cycle. The analytical solutions are plotted. Under influence of these effects, pulse did not maintain its initial shape.
Keywords: Adomian method, nonlinear Schrödinger equation, ultrashort pulse propagation