zbMATH — the first resource for mathematics

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.

MSC:
 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: