Group analysis of general Burgers-Korteweg-de Vries equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000017" target="_blank" >RIV/47813059:19610/17:A0000017 - isvavai.cz</a>

Výsledek na webu

<a href="http://aip.scitation.org/doi/10.1063/1.4997574" target="_blank" >http://aip.scitation.org/doi/10.1063/1.4997574</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.4997574" target="_blank" >10.1063/1.4997574</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Group analysis of general Burgers-Korteweg-de Vries equations

Popis výsledku v původním jazyce

The complete group classification problem for the class of (1+1)-dimensional rth order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of r greater than or equal to two. We find the equivalence groupoids of this class and its various subclasses obtained by gauging equation coefficients with equivalence transformations. Showing that this class and certain gauged subclasses are normalized in the usual sense, we reduce the complete group classification problem for the entire class to that for the selected maximally gauged subclass, and it is the latter problem that is solved efficiently using the algebraic method of group classification. Similar studies are carried out for the two subclasses of equations with coefficients depending at most on the time or space variable, respectively. Applying an original technique, we classify Lie reductions of equations from the class under consideration with respect to its equivalence group. Studying alternative gauges for equation coefficients with equivalence transformations allows us not only to justify the choice of the most appropriate gauge for the group classification but also to construct for the first time classes of differential equations with nontrivial generalized equivalence group such that equivalence-transformation components corresponding to equation variables locally depend on nonconstant arbitrary elements of the class. For the subclass of equations with coefficients depending at most on the time variable, which is normalized in the extended generalized sense, we explicitly construct its extended generalized equivalence group in a rigorous way. The new notion of effective generalized equivalence group is introduced.

Název v anglickém jazyce

Group analysis of general Burgers-Korteweg-de Vries equations

Popis výsledku anglicky

The complete group classification problem for the class of (1+1)-dimensional rth order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of r greater than or equal to two. We find the equivalence groupoids of this class and its various subclasses obtained by gauging equation coefficients with equivalence transformations. Showing that this class and certain gauged subclasses are normalized in the usual sense, we reduce the complete group classification problem for the entire class to that for the selected maximally gauged subclass, and it is the latter problem that is solved efficiently using the algebraic method of group classification. Similar studies are carried out for the two subclasses of equations with coefficients depending at most on the time or space variable, respectively. Applying an original technique, we classify Lie reductions of equations from the class under consideration with respect to its equivalence group. Studying alternative gauges for equation coefficients with equivalence transformations allows us not only to justify the choice of the most appropriate gauge for the group classification but also to construct for the first time classes of differential equations with nontrivial generalized equivalence group such that equivalence-transformation components corresponding to equation variables locally depend on nonconstant arbitrary elements of the class. For the subclass of equations with coefficients depending at most on the time variable, which is normalized in the extended generalized sense, we explicitly construct its extended generalized equivalence group in a rigorous way. The new notion of effective generalized equivalence group is introduced.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

58

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

„081511-1“-„081511-37“

Kód UT WoS článku

000409197200012

EID výsledku v databázi Scopus

2-s2.0-85028682369