相关论文: On the Schr\"odinger flows
In this paper, we study the long time dynamics of small solutions to Schr\"odinger map flows from $\Bbb R$ to Riemannian surfaces. The results are threefold. (i) We prove that for general Riemannian surface targets the points with some…
Recently we have reanalyzed the consistency of the solutions of the space fractional Schr\"odinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
On a compact Riemannian manifold, we study the various dynamical properties of the Schr\"odinger flow $(e^{it\Delta/2})$, through the notion of semiclassical measures and the quantum-classical correspondence between the Schr\"odinger…
We study a class of quasi-linear Schr\"odinger equations arising in the theory of superfluid film in plasma physics. First, using gauge transforms and a derivation process we solve, under some regularity assumptions, the Cauchy problem.…
A geometric flow on $(2,2)$-forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. The existence of solutions for a short time is established,…
We obtained a new solution of Schrodinger equation by the method of Euclidean approach (Wick rotation). This is a wave motion which is fluctuating.
We examine a recently-proposed family of nonlinear Schr\"odinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole…
In this paper, we introduce a new notion named as Schr\"odinger soliton. So-called Schr\"odinger solitons are defined as a class of special solutions to the Schr\"odinger flow equation from a Riemannian manifold or a Lorentzian manifold $M$…
We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.
This article is concerned with one dimensional dispersive flows with cubic nonlinearities on the real line. In a very recent work, the authors have introduced a broad conjecture for such flows, asserting that in the defocusing case, small…
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.
In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutions cannot be too small. We also use these…
In this paper, we define a class of new geometric flows on a complete Riemannian manifold. The new flow is related to the generalized (third order) Landau-Lifishitz equation. On the other hand it could be thought of a special case of the…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
In this note we construct an infinite family of ancient solutions to the Curve Shortening Flow which span the halfplane.