On the Analytical Approach to the N-Fold Bäcklund Transformation of Davey-Stewartson Equation

Introduction: Inverse scattering transform holds a central place in the analysis of nonlinear integrable system in either (1+1)or (2+1)-dimensions [1]. On the other hand it has been found that explicit soliton solutions can also be obtained by the use of Bäcklund transformations in a much easier way [2]. These Bäcklund transformations are also useful in proving the superposition formulae for these solutions. There have been many attempts to construct explicit N -soliton solutions for nonlinear integrable system either by Bäcklund transformations or the inverse scattering method. A separate and elegant approach was developed by Zakharov et al [3] which relied on the pole structure of the Lax eigenfunction and use of projection operators. In this letter we have used an approach similar to that of Zakharov et al but have generated a formulae for the N -fold BT of the nonlinear field variables occurring in the (2+1)-dimensional Davey-Stewartson equation [4]. Our approach is very similar to that of gauge transformation repeatedly applied to any particular seed solution. Lastly we demonstrate how non-trivial solutions are generated by starting with known trivial ones.