Solution of the nonlinear Schrödinger equation with defocusing strength nonlinearities through the Laplace-Adomian decomposition method

DOI10.1007/s40819-017-0325-5zbMath1397.65218arXiv1801.00809OpenAlexW2590112442MaRDI QIDQ1792232

O. González-Gaxiola, R. Bernal-Jaquez, Pedro Franco

Publication date: 11 October 2018

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00809

zbMATH Keywords

Laplace transformnonlinear Schrödinger equationAdomian decomposition methodBose-Einstein condensate

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (2)

Numerical treatments of the nonlinear coupled time‐fractional Schrödinger equations ⋮ Bright optical solitons with polynomial law of nonlinear refractive index by Adomian decomposition scheme

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Laplace Adomian decomposition method for solving a model for HIV infection of \(CD4^{+}T\) cells
• Analytic treatment of linear and nonlinear Schrödinger equations: a study with homotopy-perturbation and Adomian decomposition methods
• Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method
• Convenient analytic recurrence algorithms for the Adomian polynomials
• New recurrence algorithms for the nonclassic Adomian polynomials
• A Laplace variational iteration strategy for the solution of differential equations
• Explicit series solutions of some linear and nonlinear Schrödinger equations via the homotopy analysis method
• The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations
• A new approach to the cubic Schrödinger equation: an application of the decomposition technique
• Solving frontier problems of physics: the decomposition method
• Decomposition methods: A new proof of convergence
• Convergence of Adomian's method applied to differential equations
• A new approach to Bratu's problem
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• A Laplace decomposition algorithm applied to a class of nonlinear differential equations
• A novel fixed point iteration method for the solution of third order boundary value problems
• New method for calculating Adomian polynomials
• A new modification of the Adomian decomposition method for linear and nonlinear operators
• New ideas for proving convergence of decomposition methods
• Exact solutions for periodic and solitary matter waves in nonlinear lattices
• A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations
• Numerical solution of Duffing equation by the Laplace decomposition algorithm
• Convergence of Adomian's Method

This page was built for publication: Solution of the nonlinear Schrödinger equation with defocusing strength nonlinearities through the Laplace-Adomian decomposition method