Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems

@inbook{50200,
   author = {Sergyeyev, Artur and Błaszak, Maciej},
   address = {Boca Raton},
   booktitle = {Nonlinear Systems and Their Remarkable Mathematical Structures},
   doi = {http://dx.doi.org/10.1201/9780429263743-2},
   edition = {1st Edition},
   editor = {Norbert Euler, Maria Clara Nucci},
   keywords = {integrable systems; Lax pairs; dispersionless systems},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Boca Raton},
   isbn = {978-0-367-20847-9},
   pages = {29-58},
   publisher = {Chapman and Hall/CRC},
   title = {Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems},
   url = {https://www.taylorfrancis.com/chapters/contact-lax-pairs-associated-3-1-dimensional-integrable-dispersionless-systems-maciej-b%C5%82aszak-artur-sergyeyev/e/10.1201/9780429263743-2},
   year = {2019}
}

TY  - CHAP
ID  - 50200
AU  - Sergyeyev, Artur - Błaszak, Maciej
PY  - 2019
TI  - Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems
VL  - Volume 2
PB  - Chapman and Hall/CRC
CY  - Boca Raton
SN  - 9780367208479
KW  - integrable systems
KW  - Lax pairs
KW  - dispersionless systems
UR  - https://www.taylorfrancis.com/chapters/contact-lax-pairs-associated-3-1-dimensional-integrable-dispersionless-systems-maciej-b%C5%82aszak-artur-sergyeyev/e/10.1201/9780429263743-2
N2  - 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.
ER  - 

SERGYEYEV, Artur a Maciej BŁASZAK. Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems. In Norbert Euler, Maria Clara Nucci. \textit{Nonlinear Systems and Their Remarkable Mathematical Structures}. 1st Edition. Boca Raton: Chapman and Hall/CRC, 2019, s.~29-58. Volume 2. ISBN~978-0-367-20847-9. Dostupné z: https://dx.doi.org/10.1201/9780429263743-2.