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ADM-Padé technique for the nonlinear lattice equations. (English) Zbl 1162.65399

Summary: ADM-Padé technique is a combination of Adomian decomposition method (ADM) and Padé approximants. We solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence rate than using ADM alone. Bell-shaped solitary solution of Belov-Chaltikian (BC) lattice and kink-shaped solitary solution of the nonlinear self-dual network equations (SDNEs) are presented. Comparisons are made between approximate solutions and exact solutions to illustrate the validity and the great potential of the technique.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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