Solutions of the Davey-Stewartson Equation with Non-Zero Boundary Condition

Abstract

The talk is linked up to the direct linearization (DL) of the DS II as given in section 5 of ref. 1, and uses the same notation. The treatment in ref. 1 is still to be supplemented by the calculation of solutions ϕ(x, y, t), ψ(x, y, t) of the DS II from the choice of measure and contour

$$\int\limits_{\rm{D}} {\int {{\rm{d\zeta (}}\ell {\rm{, }}\ell '{\rm{)}}} = \sum\limits_{{\rm{n = 1}}}^{\rm{N}} {\sum\limits_{{\rm{m = 1}}}^{\rm{M}} {{{\rm{c}}_{{\rm{nm}}}}} {{({1 \over {2{\rm{\pi i}}}})}^2}} \oint {{\rm{d}}\ell } {1 \over {\ell - {\rm{i}}{{\rm{p}}_{\rm{n}}}}}\oint {{\rm{d}}\ell } '{1 \over {\ell ' - {\rm{i}}{{\rm{q}}_{\rm{m}}}}}} .$$

(1)