## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Group Classification of Variable Coefficient $K(m,n)$ Equations

#### Abstract

Lie symmetries of $K(m,n)$ equations with time-dependent coefficients are classified. Group classification is presented up to widest possible equivalence groups, the usual equivalence group of the whole class for the general case and the conditional equivalence groups for special values of the exponents $m$ and $n$. Examples on reduction of $K(m,n)$ equations (with initial and boundary conditions to nonlinear ordinary differential equations (with initial conditions) are presented.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815704

Digital Object Identifier
doi:10.7546/giq-15-2014-106-116

Mathematical Reviews number (MathSciNet)
MR3287751

Zentralblatt MATH identifier
1316.82029

#### Citation

Charalambous, Kyriakos; Vaneeva, Olena; Sophocleous, Christodoulos. Group Classification of Variable Coefficient $K(m,n)$ Equations. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 106--116, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-106-116. https://projecteuclid.org/euclid.pgiq/1436815704