%0 Journal Article 
%A Rosa Silva, Rafael de la
%A Recio Rodríguez, Elena
%A Garrido Letrán, Tamara María
%A Bruzón Gallego, María de los Santos
%T Lie symmetry analysis of (2+1)-dimensional KdV equations with variable coefficients
%D 2020
%@ 0020-7160
%U http://hdl.handle.net/10498/33276
%X 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.
%K Variable-coefficient KdV equations
%K solvable symmetry algebras
%K symmetries
%K symmetry reductions
%~ Universidad de Cádiz