@misc{10498/33276,
year = {2020},
url = {http://hdl.handle.net/10498/33276},
abstract = {In this paper, symmetry groups are used to obtain symmetry reductions
of (2+1)-dimensional KdV equations with variable coefficients. Despite
the fact that these equations emerge in a nonlocal form, by using suitable
transformations, they can be written as systems of partial differential
equations, and in potential form, as fourth-order partial differential
equations. We show that the point symmetries of the potential equation
involve a large number of arbitrary functions. Moreover, these symmetries
are used to transform the fourth-order partial differential equations
into (1+1)-dimensional fourth-order differential equations. Furthermore,
we have determined all two-dimensional solvable symmetry subalgebras,
under certain restrictions, which the potential equation admits. Finally, by
way of example, taking into account a two-dimensional abelian subalgebra,
we obtain a direct reduction of the potential equation to an ordinary
differential equation.},
publisher = {Taylor and Francis},
keywords = {Variable-coefficient KdV equations},
keywords = {solvable symmetry algebras},
keywords = {symmetries},
keywords = {symmetry reductions},
title = {Lie symmetry analysis of (2+1)-dimensional KdV equations with variable coefficients},
doi = {10.1080/00207160.2019.1599107},
author = {Rosa Silva, Rafael de la and Recio Rodríguez, Elena and Garrido Letrán, Tamara María and Bruzón Gallego, María de los Santos},
}