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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...
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...