Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator

Abstract

In this paper, an effective analytical scheme based on Sumudu transform known as homotopy perturbation Sumudu transform method (HP-STM) is employed to find numerical solutions of time fractional Schrödinger equations with harmonic oscillator.These nonlinear time fractional Schrödinger equations describe the various phenomena in physics such as motion of quantum oscillator, lattice vibration, propagation of electromagnetic waves, fluid flow, etc. The main objective of this study is to show the effectiveness of HPSTM, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results reveal that proposed scheme is a powerful tool for study large class of problems. This study shows that the results obtained by the HPSTM are accurate and effective for analysis the nonlinear behaviour of complex systems and efficient over other available analytical schemes.

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

“…Therefore, there has been significant progress in the development of diverse schemes for treating NLSEs and nonlinear partial differential equations (NPDEs) in the general case. For approximate schemes, we cite the Adomian decomposition method [5,6], collocation method [7], homotopy perturbation method [8], homotopy analysis method [9], reduced differential transform method [10,11], q-homotopy analysis method [12], variational iteration method [13], reproducing kernel Hilbert space method [14], iterative Shehu transform method [15], and residual power series method [16,17]. While constructing an exact analytic solution is of more importance since this can provide the best understanding of the model's nature to be processed in an efficient way, researchers have developed various powerful tools to analyze NPDEs.…”