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We discuss a class of normal forms of the completely resonant non–linear Schr¨odinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further anal...
We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(...
The plane wave stability properties of the conservative schemes of Besse and Fei et al. for the cubic Schr\"{o}dinger equation are analysed. Although the two methods possess many of the same conserva...
In this paper, we consider the Cauchy problem of Nonlinear Schr¨odinger equationiut + u = λ1|u|p1u + λ2|u|p2u, t ∈ R, x ∈ RN u(0, x) = ϕ(x), x ∈ RN,where N ≥ 3, 0 < p1 < p2 < 4 N−2 , λ1 ...
In this paper, we consider the two component derivative nonlinear Schr\"{o}dinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a ...
We solve the unique continuation property: If u is a solution of the higher order nonlinear Schrödinger equation with constant coefficients with t1 < t2 which is sufficiently smooth and such that...

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