The BB acklund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its eeects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vortex lament ow (also known as the Localized Induction Equation). In doing so...

The Miura and anti-Miura transformations between the q-deformed KP modified hierarchies are investigated in this paper. Then auto-Backlund for constructed through combinations of transformations. And corresponding results also generalized to constrained cases. At last, some examples given.

We prove the Bianchi permutability (existence of superposition principle) Backlund transformations for asymmetric quad-equations. Such equations and their form 3D consis...

The correspondance is established between the sigma models , the minimal surfaces and the Monge-Ampére equation. The Lax-Pairs of the minimality condition of the minimal surfaces and the MongeAmpére equations are given. Existance of infinitely many nonlocal conservation laws is shown and some Backlund transformations are also given.

After a review of the basic results concerning theN = 1, 2 supersymmetric extensions of the Korteweg-de Vries equation, with a pedagogical presentation of the superspace techniques, we discuss some basic open problems mainly in relation with the N = 2 extensions. 07/99 1 Work supported by NSERC (Canada) and FCAR (Québec) 2 Talk presented at AARMS-CRM Workshop on Backlund and Darboux Transformat...