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Application of He’s variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM. (English) Zbl 1120.65107
Summary: Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called J.-H. He’s variational iteration method [Int. J. Non-Linear Mech. 34, No. 4, 699–708 (1999; Zbl 1342.34005)] is introduced to be applied to solve nonlinear Jaulent-Miodek, coupled Korteweg-de Vries (KdV) and coupled modified KdV equations. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with exact solutions.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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