Analytic treatment of linear and nonlinear Schrödinger equations: a study with homotopy-perturbation and Adomian decomposition methods
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Publication:552578
DOI10.1016/j.physleta.2007.07.065zbMath1217.81069OpenAlexW1976349702MaRDI QIDQ552578
A. Sadighi, Davood Domairry Ganji
Publication date: 26 July 2011
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physleta.2007.07.065
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbation theories for operators and differential equations in quantum theory (81Q15) Exactly and quasi-solvable systems arising in quantum theory (81U15)
Related Items (31)
Fixed-term homotopy ⋮ NUMERICAL SOLUTIONS FOR THE NONLINEAR FORNBERG–WHITHAM EQUATION BY HE'S METHODS ⋮ Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations ⋮ A study on the \(d\)-dimensional Schrödinger equation with a power-law nonlinearity ⋮ A new numerical scheme for the nonlinear Schrödinger equation with wave operator ⋮ Nonlinear spin dynamics of a couple of nonlinear Schrödinger's equations by the improved form of an analytical method ⋮ A novel approach for solving linear and nonlinear time-fractional Schrödinger equations ⋮ An approximate analytical solution of the nonlinear Schrödinger equation with harmonic oscillator using homotopy perturbation method and Laplace-Adomian decomposition method ⋮ Exact solutions for non-linear Schrödinger equations by differential transformation method ⋮ The solvability of first type boundary value problem for a Schrödinger equation ⋮ Approximate solutions to time-fractional Schrödinger equation via homotopy analysis method ⋮ An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method ⋮ A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity ⋮ Nonlinear Klein-Gordon and Schrödinger equations by the projected differential transform method ⋮ An approximate analytic solution of the heat conduction equation at nanoscale ⋮ Application of Adomian decomposition method to bounded and unbounded Stokes' problems ⋮ Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator ⋮ Approximate explicit solutions of Orr-Sommerfeld equations and heat transfer in a geometry with variable cross section by he's methods and comparison with the ADM and DTM ⋮ Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system ⋮ Approximate analytical solutions of Schnakenberg systems by homotopy analysis method ⋮ A new approximate method and its convergence for a strongly nonlinear problem governing electrohydrodynamic flow of a fluid in a circular cylindrical conduit ⋮ A series solution of the Cauchy problem for the generalized \(d\)-dimensional Schrödinger equation with a power-law nonlinearity ⋮ Exact analytic solutions of Schrödinger linear and nonlinear equations ⋮ Explicit series solutions of some linear and nonlinear Schrödinger equations via the homotopy analysis method ⋮ Solution of the nonlinear Schrödinger equation with defocusing strength nonlinearities through the Laplace-Adomian decomposition method ⋮ Generalized homotopy method for solving nonlinear differential equations ⋮ An approximation of the analytical solution of the linear and nonlinear integro-differential equations by homotopy perturbation method ⋮ An application of exp-function method to approximate general and explicit solutions for nonlinear Schrödinger equations ⋮ A new modification of He's homotopy perturbation method for rapid convergence of nonlinear undamped oscillators ⋮ Comparison of energy balance period with exact period for arising nonlinear oscillator equations. (He's energy balance period for nonlinear oscillators with and without discontinuities.) ⋮ New exact solutions for seventh-order Sawada-Kotera-Ito, Lax and Kaup-Kupershmidt equations using Exp-function method
Cites Work
- Variational iteration method -- a kind of non-linear analytical technique: Some examples
- Exp-function method for nonlinear wave equations
- Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder
- Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
- Exact solutions for heat-like and wave-like equations with variable coefficients.
- A new algorithm for calculating Adomian polynomials for nonlinear operators
- A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
- Homotopy perturbation method for bifurcation of nonlinear problems
- Homotopy perturbation method: a new nonlinear analytical technique
- The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
- A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
- Adomian decomposition method for a reliable treatment of the Bratu-type equations
- A numerical solution of the coupled sine-Gordon equation using the modified decomposition method
- Blow-up solutions obtained using the decomposition method
- New periodic solutions for nonlinear evolution equations using Exp-function method
- Inverse problem of diffusion equation by He's homotopy perturbation method
- Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method
- SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
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