Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems
Abstract
We review the recent approach to the construction of (3+1)-dimensional integrable dispersionless partial differential systems based on their contact Lax pairs and the related -matrix theory for the Lie algebra of functions with respect to the contact bracket. We discuss various kinds of Lax representations for such systems, in particular, linear nonisospectral contact Lax pairs and nonlinear contact Lax pairs as well as the relations among the two. Finally, we present a large number of examples with finite and infinite number of dependent variables, as well as the reductions of these examples to lower-dimensional integrable dispersionless systems.
Keywords
Cite
@article{arxiv.1901.05181,
title = {Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems},
author = {M. Blaszak and A. Sergyeyev},
journal= {arXiv preprint arXiv:1901.05181},
year = {2019}
}
Comments
25 pages, invited contribution to the book Nonlinear Systems and Their Remarkable Mathematical Structures, vol. 2, CRC Press, Taylor & Francis Group; survey based on arXiv:1401.2122 and arXiv:1605.07592