Cauchy problem for integrable discrete equations on quad-graphs

Details Cauchy problem for integrable discrete equations on quad-graphs Cauchy problem for integrable discrete equations on quad-graphs

2002-11-21

arxiv.org/abs/math-ph/0211054v1

Physics

Mathematical Physics

30 pages, 24 figures

Scientific paper

Initial value problems for the integrable discrete equations on quad-graphs are investigated. A geometric criterion of the correctness of such a problem is found. The effects of the interaction of the solutions with the localized defects in the regular square lattice are discussed for the discrete potential KdV and linear wave equations. The examples of kinks and solitons on various quad-graphs, including quasiperiodic tilings, are presented.

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