相关论文: On the Schr\"odinger flows
In this paper, we study a Schr\"odinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization…
In this paper we give new estimates for the solution to the Schr\"odinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces.
Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.
A nonlinear Schr\"odinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can…
The wave equation in quantum mechanics and its general solution in the phase space are obtained.
On the basis of analytical results, we present a numerical example that indicates inconsistency of a widely used ansatz with cubically nonlinear Schr\"odinger equation.
We clarify existence and non-existence of graph-like forward self-similar solutions to the planar surface diffusion equations.
On a smooth closed Riemannian manifold, we show short time existence of smooth solutions to the $(\alpha,\beta)$-Ricci-Yamabe flow, which is a natural generalization of the Ricci flow and the Yamabe flow. We also establish some long time…
We give a survey of various existence results for minimal Lagrangian graphs. We also discuss the mean curvature flow for Lagrangian graphs.
We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…
We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schr\"odinger equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness…
The paper deals with locally bounded solutions of a Schilling's problem.
A method to find exact solutions to nonlinear Schr\"odinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati…
This paper is devoted to the analysis of blow-up solutions for the fractional nonlinear Schr\"odinger equation with combined power-type nonlinearities \[ i\partial_t u-(-\Delta)^su+\lambda_1|u|^{2p_1}u+\lambda_2|u|^{2p_2}u=0, \] where…
In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and…
In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…