@article{28091,
   author = {Opanasenko, Stanislav and Bihlo, Alexander and Popovych, Roman},
   article_location = {USA},
   article_number = {8},
   doi = {http://dx.doi.org/10.1063/1.4997574},
   keywords = {Burgers-KdV equation; Group classification; Lie reduction},
   language = {eng},
   issn = {0022-2488},
   journal = {Journal of Mathematical Physics},
   title = {Group analysis of general Burgers-Korteweg-de Vries equations},
   url = {http://aip.scitation.org/doi/10.1063/1.4997574},
   volume = {58},
   year = {2017}
}

TY  - JOUR
ID  - 28091
AU  - Opanasenko, Stanislav - Bihlo, Alexander - Popovych, Roman
PY  - 2017
TI  - Group analysis of general Burgers-Korteweg-de Vries equations
JF  - Journal of Mathematical Physics
VL  - 58
IS  - 8
SP  - „081511-1“-„081511-37“
EP  - „081511-1“-„081511-37“
PB  - American Institute of Physics
SN  - 0022-2488
KW  - Burgers-KdV equation
KW  - Group classification
KW  - Lie reduction
UR  - http://aip.scitation.org/doi/10.1063/1.4997574
L2  - http://aip.scitation.org/doi/10.1063/1.4997574
N2  - 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.
ER  - 

OPANASENKO, Stanislav, Alexander BIHLO a Roman POPOVYCH. Group analysis of general Burgers-Korteweg-de Vries equations. \textit{Journal of Mathematical Physics}. USA: American Institute of Physics, roč.~58, č.~8, s.~„081511-1“-„081511-37“, 37 s. ISSN~0022-2488. doi:10.1063/1.4997574. 2017.