Solving Nonlinear Schrodinger Equation with Variable Coefficient Using Homotopy Perturbation Method

2016 ◽  
pp. 253-262
Author(s):  
Nazatulsyima Mohd Yazid ◽  
Kim Gaik Tay ◽  
Yaan Yee Choy ◽  
Azila Md Sudin
Keyword(s):  
Schrödinger Equation ◽  
Perturbation Method ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation

scholarly journals An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Emad K. Jaradat ◽  
Omar Alomari ◽  
Mohammad Abudayah ◽  
Ala’a M. Al-Faqih
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM and HPM methods, in addition to comparing and analyzing both solutions.

Riemann–Hilbert approach and multi-soliton solutions of a variable-coefficient fifth-order nonlinear Schrödinger equation with N distinct arbitrary-order poles

2021 ◽  
pp. 2150194
Author(s):  
Zhi-Qiang Li ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Jin-Jie Yang
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Arbitrary Order ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Fifth Order

Based on inverse scattering transformation, a variable-coefficient fifth-order nonlinear Schrödinger equation is studied through the Riemann–Hilbert (RH) approach with zero boundary conditions at infinity, and its multi-soliton solutions with [Formula: see text] distinct arbitrary-order poles are successfully derived. By deriving the eigenfunction and scattering matrix, and revealing their properties, a RH problem (RHP) is constructed based on inverse scattering transformation. Via solving the RHP, the formulae of multi-soliton solutions are displayed when the reflection coefficient possesses [Formula: see text] distinct arbitrary-order poles. Finally, some appropriate parameters are selected to analyze the interaction of multi-soliton solutions graphically.

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