caa a22 4500 467954208 CHVBK 20180405193745.0 cr unu---uuuuu 170328e20041101xx s 000 0 eng 10.1007/s10440-005-4557-8 doi (NATIONALLICENCE)springer-10.1007/s10440-005-4557-8 (NATIONALLICENCE)springer-10.1007/s10440-004-5557-9 Cauchy problem for integrable discrete equations on quad-graphs [Elektronische Daten] [V. Adler, A. Veselov] 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. Kluwer Academic Publishers, 2004 Cauchy problem nationallicence quad-graph nationallicence discrete integrable equations nationallicence Adler V. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany aut Veselov A. Loughborough University, LE11 3TU, Loughborough, Leicestershire, UK aut Acta Applicandae Mathematica Kluwer Academic Publishers 84/2(2004-11-01), 237-262 0167-8019 84:2<237 2004 84 10440 https://doi.org/10.1007/s10440-005-4557-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-005-4557-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Veselov A. Loughborough University, LE11 3TU, Loughborough, Leicestershire, UK aut NATIONALLICENCE 700 1- Adler V. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 84/2(2004-11-01), 237-262 0167-8019 84:2<237 2004 84 10440 NATIONALLICENCE 700 1- Veselov A. Loughborough University, Loughborough, Leicestershire LE11 3TU, UK and Landau Institute for Theoretical Physics, Russia aut NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-004-5557-9 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer