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Explicit series solutions of some linear and nonlinear Schrödinger equations via the homotopy analysis method. (English) Zbl 1221.35389
Summary: By means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \(\hbar\), that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems.

35Q55 NLS equations (nonlinear Schrödinger equations)
35C10 Series solutions to PDEs
35J10 Schrödinger operator, Schrödinger equation
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
Full Text: DOI
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