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Some relatively new techniques for nonlinear problems. (English) Zbl 1184.35280
Summary: This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we focus on the variational iteration method and its modifications, the homotopy perturbation method, the parameter expansion method, and exp-function method. These relatively new but very reliable techniques proved useful for solving a wide class of nonlinear problems and are capable to cope with the versatility of the physical problems. Several examples are given to reconfirm the efficiency of these algorithms. Some open problems are also suggested for future research work.
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
65Z05Applications of numerical analysis to physics
35A30Geometric theory for PDE, characteristics, transformations
35A24Methods of ordinary differential equations for PDE
35A15Variational methods (PDE)
35-02Research monographs (partial differential equations)