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Cauchy Problem for Integrable Discrete Equations on Quad-Graphs

Cauchy Problem for Integrable Discrete Equations on Quad-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Cauchy Problem for Integrable Discrete Equations on Quad-Graphs

Acta Applicandae Mathematicae , Volume 84 (2): 26 – Nov 1, 2004

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References (39)

Publisher
Springer Journals
Copyright
2004 Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-004-5557-9
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Applicandae MathematicaeSpringer 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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