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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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
65Z05 Applications to the sciences
35A30 Geometric theory, characteristics, transformations in context of PDEs
35A24 Methods of ordinary differential equations applied to PDEs
35A15 Variational methods applied to PDEs
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
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References:

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