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Normal Form for the Schrödinger equation with analytic non--linearities
Normal Form Schrö dinger equation analytic non--linearities
2011/1/17
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...
Surface Gap Soliton Ground States for the Nonlinear Schrödinger Equation
Surface Gap Soliton Ground States the Nonlinear Schrö dinger Equation
2010/11/18
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(...
Plane wave stability of some conservative schemes for the cubic Schrödinger equation
Plane wave conservative schemes the cubic Schrö dinger equation
2010/11/11
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...
Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
Nonlinear Schr¨odinger equation Global existence Scattering property
2010/11/29
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 ...
Darboux transformation for two component derivative nonlinear Schrödinger equation
Darboux transformation solitons DNLS
2010/4/8
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 ...
On the Unique Continuation Property for the Higher Order Nonlinear Schrödinger Equation With Constant Coefficients
Higher order nonlinear Schrö dinger equation unique continuation property
2010/2/26
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...