Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

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.