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Cauchy problem for integrable discrete equations on quad-graphs

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preprint
posted on 25.07.2005, 10:52 by V.E. Adler, Alexander Veselov
Initial value problems for the integrable discrete equations on quadgraphs 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.

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  • Science

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  • Mathematical Sciences

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587423 bytes

Publication date

2003

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This pre-print has been submitted, and accepted, to the journal Acta Applicandae Mathematicae. The deinitive version: ADLER, V.E. and VESELOV, A.P., 2004. Cauchy problem for integrable discrete equations on quad-graphs. Acta Applicandae Mathematicae, 84(2),pp.237-262 is available at www.springerlink.com.

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en

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