Multidimensional integrable systems from contact geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000189" target="_blank" >RIV/47813059:19610/25:A0000189 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s40590-024-00703-7" target="_blank" >https://link.springer.com/article/10.1007/s40590-024-00703-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40590-024-00703-7" target="_blank" >10.1007/s40590-024-00703-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multidimensional integrable systems from contact geometry

Popis výsledku v původním jazyce

Upon having presented a bird’s eye view of history of integrable systems, we give a brief review of certain recent advances in the longstanding problem of search for partial differential systems in four independent variables, often referred to as (3+1)-dimensional or 4D systems, that are integrable in the sense of soliton theory. Namely, we review a recent construction for a large new class of (3+1)-dimensional integrable systems with Lax pairs involving contact vector fields. This class contains inter alia two infinite families of such systems, thus establishing that there is significantly more integrable (3+1)-dimensional systems than it was believed for a long time. In fact, the construction under study yields (3+1)-dimensional integrable generalizations of many well-known dispersionless integrable (2+1)-dimensional systems like the dispersionless KP equation, as well as a first example of a (3+1)-dimensional integrable system with an algebraic, rather than rational, nonisospectral Lax pair. To demonstrate the versatility of the construction in question, we employ it here to produce novel integrable (3+1)-dimensional generalizations for the following (2+1)-dimensional integrable systems: dispersionless BKP, dispersionless asymmetric Nizhnik–Veselov–Novikov, dispersionless Gardner, and dispersionless modified KP equations, and the generalized Benney system.

Název v anglickém jazyce

Multidimensional integrable systems from contact geometry

Popis výsledku anglicky

Upon having presented a bird’s eye view of history of integrable systems, we give a brief review of certain recent advances in the longstanding problem of search for partial differential systems in four independent variables, often referred to as (3+1)-dimensional or 4D systems, that are integrable in the sense of soliton theory. Namely, we review a recent construction for a large new class of (3+1)-dimensional integrable systems with Lax pairs involving contact vector fields. This class contains inter alia two infinite families of such systems, thus establishing that there is significantly more integrable (3+1)-dimensional systems than it was believed for a long time. In fact, the construction under study yields (3+1)-dimensional integrable generalizations of many well-known dispersionless integrable (2+1)-dimensional systems like the dispersionless KP equation, as well as a first example of a (3+1)-dimensional integrable system with an algebraic, rather than rational, nonisospectral Lax pair. To demonstrate the versatility of the construction in question, we employ it here to produce novel integrable (3+1)-dimensional generalizations for the following (2+1)-dimensional integrable systems: dispersionless BKP, dispersionless asymmetric Nizhnik–Veselov–Novikov, dispersionless Gardner, and dispersionless modified KP equations, and the generalized Benney system.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Boletín de la Sociedad Matemática Mexicana

ISSN

1405-213X

e-ISSN

2296-4495

Svazek periodika

31

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

14

Strana od-do

„26-1“-„26-14“

Kód UT WoS článku

001389404600002

EID výsledku v databázi Scopus

2-s2.0-85214025252