相关论文: Remarks on the Schrodinger equation

A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and…

We study the nonlinear Schrodinger equations with a linear potential. A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential.

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.

We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger…

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…

By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…

We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…

This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…

For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…

We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…

The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…

Proceeding from the hydrodynamic approach, we construct exact solutions to nonlinear Schr\"odinger equation with special properties. The solutions describe collapse, in finite time, and scattering, over infinite time, of wave packets. They…

In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.

We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…

The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…

We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…

A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schr\"{o}dinger equation. An explicit expression for its solution is given under certain assumptions and it is shown that it entails…