Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential
نویسندگان
چکیده
We review different properties related to the Cauchy problem for the (nonlinear) Schrödinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.
منابع مشابه
On the Cauchy problem in Sobolev spaces for nonlinear Schrodinger equations with potential
We consider the Cauchy problem for nonlinear Schrödinger equations in the presence of a smooth, possibly unbounded, potential. No assumption is made on the sign of the potential. If the potential grows at most linearly at infinity, we construct solutions in Sobolev spaces (without weight), locally in time. Under some natural assumptions, we prove that the H-solutions are global in time. On the ...
متن کاملSolutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...
متن کاملPeriodic Wave Shock solutions of Burgers equations
In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...
متن کاملNvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition
Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...
متن کاملCALCULATION OF NON LIFTING POTENTIAL FLOW USING DESINGULARIZED CAUCHY\'S FORMULA
This paper discusses the disturbance velocity and potential as well as the total velocity formulation for non lifting potential flow problem. The problem is derived based on the Cauchy method formulation. The adding and subtracting back technique is used to desingularize the integral equations. The desingularized boundary integral equations are then discretized. The discretized equations can be...
متن کامل