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The research by V.A. was partly supported by RFBR grant 02-01-00144
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is grateful to S.P. Novikov who stimulated his interest to the problems on the graphs
Abstract Initial value problems for the integrable discrete equations on quad-graphs are investigated. We give a geometric criterion of when such a problem is well-posed. In the basic example of the discrete KdV equation an effective integration scheme based on the matrix factorization problem is proposed and the interaction of the solutions with the localized defects in the regular square lattice are discussed in details. The examples of kinks and solitons on various quad-graphs, including quasiperiodic tilings, are presented.
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 1, 2004
Keywords: Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
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