Analytic treatment of linear and nonlinear Schrödinger equations: a study with homotopy-perturbation and Adomian decomposition methods. (English) Zbl 1217.81069

Sadighi, A.; Ganji, D. D.

Phys. Lett., A 372, No. 4, 465-469 (2008).

Summary: In this work, two powerful analytical methods, called homotopy-perturbation method (HPM) and Adomian decomposition method (ADM) are introduced to obtain the exact solutions of linear and nonlinear Schrödinger equations. The main objective is to propose alternative methods of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that these methods are very efficient and convenient and can be applied to a large class of problems. The comparison of the methods shows that although the numerical results of these methods are the same, HPM is much easier, more convenient and efficient than ADM.

MSC:

81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55	NLS equations (nonlinear Schrödinger equations)
81Q15	Perturbation theories for operators and differential equations in quantum theory
81U15	Exactly and quasi-solvable systems arising in quantum theory

Keywords:

Schrödinger equations; homotopy-perturbation method; Adomian decomposition method

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