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Group analysis of KdV equation with time dependent coefficients. (English) Zbl 1197.35231
Summary: We study the generalized KdV equation having time dependent variable coefficients of the damping and dispersion from the Lie group-theoretic point of view. Lie group classification with respect to the time dependent coefficients is performed. The optimal system of one-dimensional subalgebras of the Lie symmetry algebras are obtained. These subalgebras are then used to construct a number of similarity reductions and exact group-invariant solutions, including soliton solutions, for some special forms of the equations.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
35C08 Soliton solutions
35C05 Solutions to PDEs in closed form
22E70 Applications of Lie groups to the sciences; explicit representations
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