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The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number k increases, known as `pollution effect' which is directly related to the phase diff...
Our work is to prove the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density $\rho_0$ is discontinuous and the i...
The nonlinear Schrodinger (NLS)type equations are very important integrable equations. In this talk, we will give a brief review for NLS type equations including NLS equation, derivative NLS equation...
In this talk, we will introduce a novel overlapping domain decomposition splitting algorithm based on a Crank--Nisolson method is developed for the stochastic NLS equation driven by a multiplicative n...
In this paper, we will discuss the mixed boundary value problems for the second order elliptic equation with rapidly oscillating coefficients in perforated domains, and will present the higher-order...
A high order finite difference-spectral method is derived for solving space fractional diffusion equations, by combining the second order finite difference method in time and the spectral Galerkin met...
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems wh...
In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle if and only if the physical mass $m$ of the scalar field and the dimension $n$ of the sp...
In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, b...
Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompress...
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equat...

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