A new integrable nonlinear equation recently derived in the domain of non linear optics is analysed in the light of Riemann-Hilbert problem. Explicit soliton solutions for the equation are obtained in case of both single and two soliton regimes. Our analysis shows how to use the Riemann-Hilbert procedure with or without utilising the symmetry of the Lax pair. c © Electronic Journal of Theoretic...

Let S be a generic C∞ CR manifold in C, l ≥ 2, and let M be a generic C∞ CR submanifold of S × C, m ≥ 1. We prescribe conditions on M so that it is the disjoint union of graphs of CR maps f : S → C. We also consider the special case where S is the boundary of a bounded, smoothly bounded open set D in C, l ≥ 2. In this case we obtain conditions which guarantee that such an f above extends to be ...