Initial value problems for quad equations

DOI10.1088/1751-8113/48/6/065204zbMATH Open1314.05202arXiv1210.1414OpenAlexW2964074385MaRDI QIDQ5176704

Publication date: 27 February 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We describe a method to construct well-posed initial value problems for not necessarily integrable equations on not necessarily simply connected quad-graphs. Although the method does not always provide a well-posed initial value problem (not all quad-graphs admit well-posed initial value problems) it is effective in the class of rhombic embeddable quad-graphs.

Full work available at URL: https://arxiv.org/abs/1210.1414

zbMATH Keywords

initial value problem integrable quad-graph

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Sensitivity, stability, parametric optimization (90C31) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Numerical methods for initial value problems involving ordinary differential equations (65L05) Graph algorithms (graph-theoretic aspects) (05C85) Connectivity (05C40) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

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