Analytic wave front set for solutions to Schrödinger equations
نویسندگان
چکیده
منابع مشابه
Analytic Wave Front Set for Solutions to Schrödinger Equations
This paper is a continuation of [MNS], where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian H0 on R . In this paper, we consider short-range type perturbations H of the Laplacian on R, and we characterize the analytic wave front set of the solution to the Schrödinger equation: ef , in terms of that of the free solution: e0f , for t < 0 in the forward ...
متن کاملWave Front Set for Solutions to Schrödinger Equations∗
We consider solutions to Schrödinger equation with variable coefficients. Let H be a Schrödinger operator and let u(t) = e−itHu0 with u0 ∈ L(R). We show that the wave front set of u0 in the nontrapping region corresponds to the wave front set of e0u(t), where H0 is the free Schrödinger operator. The correspondence is given by the wave operator for the classical mechanical scattering.
متن کاملGeneralized solitary wave solutions for the Klein-Gordon-Schrödinger equations
Some new generalized solitary solutions of the Klein–Gordon–Schrödinger equations are obtained using the Exp-function method, which include some known solutions obtained by the F-expansion method and the homogeneous balance method in the open literature as special cases. It is shown that the Exp-function method is a straight, concise, reliable and promising mathematical tool for solving nonline...
متن کاملSpeed of wave-front solutions to hyperbolic reaction-diffusion equations.
The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine ...
متن کاملPropagation of the Homogeneous Wave Front Set for Schrödinger Equations∗
In this paper we study the propagation of singularity for Schrödingertype equations with variable coefficients. We introduce a new notion of wave propagation set, the homogeneous wave front set, and it propagates along straight lines with finite speed away from x 6= 0. Then we show that it is related to the wave front set in a natural way. These results may be considered as a refinement of the ...
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: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.06.002