Backlund transformation for the variable coefficient korteweg-de vries equation

Abstract

We present a Backlund transformation for the variable coefficient Korteweg-de Vries equation. The permutability property of the transformation is established, and the permutability relation is found to take the same form as that given by Wahlquist and Estabrook for the constant coefficient Korteweg-de Vries equation. It is shown that, with the choice of a constant solution, the Backlund transformation only generates constant solutions, which is in sharp contrast to the corresponding situation for the constant coefficient Korteweg-de Vries equation for which N soliton solutions are generated.

Keywords:

• Backlund transformation
• variable coefficient KdV equation

AMS(MOS):

• 35Q20