CLASSICAL AND NONCLASSICAL SYMMETRY REDUCTIONS OF THE SCHWARZ-KORTEWEG-DE VRIES EQUATION IN (2+1) DIMENSIONS
- RAMÍREZ, J.
- BRUZÓN, M. S.
- MURIEL, C.
- GANDARIAS, M. L.
ISBN: 978-981-238-241-2
Year of publication: 2003
Pages: 210-216
Type: Conference paper
Abstract
In this paper we obtain reductions and exact solutions of a (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries equation. These reductions are derived by using the classical Lie method of infinitesimal transformations and the nonclassical method. All these reduced ODEs are reduced to second order ODEs. The corresponding solutions of the (2 + 1)-dimensional equation involve two arbitrary functions. These solutions exhibit a wide variety of qualitative behaviour. Among the most interesting solutions are the soliton solutions. These soliton solutions evolves in a more general form than the soliton solutions obtainable by Lie classical reductions.