Original Articles

Approximate Symmetries of the Boussinesq Equation

Published in: Quaestiones Mathematicae
Volume 26 , issue 1 , 2003 , pages: 1–14

DOI: 10.2989/16073600309486039

Author(s): V.A. Baikov , S.A. Kordyukova

Keywords: THE BOUSSINESQ EQUATION , THE LINEAR WAVE EQUATION , APPROXIMATE SYMMETRIES , LIE-B&UML , ACKLUND TRANSFORMATIONS , INTEGRAL-DIFFERENTIAL TRANSFORMATIONS , APPROXIMATELY , INVARIANT SOLUTIONS

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Abstract

In this paper we show that all exact symmetries of the linear wave equation are inherited by the Boussinesq type equation with a small parameter as approximate symmetries in any order of precision. We find an approximate integraldifferential transformation of any order of precision, which transforms the Boussinesq type equation into the linear wave equation. Using the transformation and the symmetries, we get approximate solutions of the Boussinesq type equation.

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