SERGYEYEV, Artur and Maciej BŁASZAK. Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems. In Norbert Euler, Maria Clara Nucci. Nonlinear Systems and Their Remarkable Mathematical Structures. 1st Edition. Boca Raton: Chapman and Hall/CRC. p. 29-58. Volume 2. ISBN 978-0-367-20847-9. doi:10.1201/9780429263743-2. 2019.
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Basic information
Original name Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems
Authors SERGYEYEV, Artur (804 Ukraine, belonging to the institution) and Maciej BŁASZAK (616 Poland, guarantor).
Edition 1st Edition. Boca Raton, Nonlinear Systems and Their Remarkable Mathematical Structures, p. 29-58, 30 pp. Volume 2, 2019.
Publisher Chapman and Hall/CRC
Other information
Original language English
Type of outcome Chapter(s) of a specialized book
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
Publication form printed version "print"
WWW Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2
RIV identification code RIV/47813059:19610/19:A0000070
Organization unit Mathematical Institute in Opava
ISBN 978-0-367-20847-9
Doi http://dx.doi.org/10.1201/9780429263743-2
Keywords in English integrable systems; Lax pairs; dispersionless systems
Tags
Links GBP201/12/G028, research and development project.
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 22/4/2021 11:22.
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 R-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.
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