##
**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 |

### Keywords:

nonlinear problems; variational iteration method; homotopy perturbation method; exp-function method
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\textit{S. T. Mohyud-Din} et al., Math. Probl. Eng. 2009, Article ID 234849, 25 p. (2009; Zbl 1184.35280)

### References:

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