Quadratic derivative nonlinear Schrödinger equations in two space dimensions
نویسندگان
چکیده
منابع مشابه
On Quadratic Derivative Schrödinger Equations in One Space Dimension
We consider the Schrödinger equation with derivative perturbation terms in one space dimension. For the linear equation, we show that the standard Strichartz estimates hold under specific smallness requirements on the potential. As an application, we establish existence of local solutions for quadratic derivative Schrödinger equations in one space dimension with small and rough Cauchy data.
متن کاملOf Nonlinear Schrödinger Equations
The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schrödinger equations of the form iψt +∆ψ + F (ψ,ψ ∗) = 0.
متن کاملSoliton interactions in perturbed nonlinear Schrödinger equations.
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schrödinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the oth...
متن کاملLong Range Scattering for Nonlinear Schrödinger Equations in One and Two Space Dimensions
We study the scattering theory for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one and two space dimensions, respectively. For example, the nonlinearities are sum of gauge invariant term and non-gauge invariant terms such as λ0|u|2u + λ1u + λ2uū + λ3ū in one dimensional case, where λ0 ∈ R and λ1, λ2, λ3 ∈ C. The scattering theory for these equations belongs to...
متن کاملNonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials.
We derive the asymptotic equations governing the evolution of a quasi-monochromatic optical pulse in a nonresonant quadratic material starting from Maxwell equations. Under rather general assumptions, equations of nonlinear Schrödinger (NLS) type with coupling to mean fields result (here called NLSM). In particular, if the incident pulse is polarized along one of the principal axes of the mater...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA
سال: 2011
ISSN: 1021-9722,1420-9004
DOI: 10.1007/s00030-011-0098-1