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Exact solutions for non-linear Schrödinger equations by differential transformation method. (English) Zbl 1211.35250
Summary: We implement relatively new, exact series method of solution known as the differential transform method for solving linear and nonlinear Schrödinger equations with initial profile. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35C10Series solutions of PDE
35A30Geometric theory for PDE, characteristics, transformations
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
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