Integrable time-dependent central potentials

Integrable Evolution Equations in Time-Dependent Domains

The Last Integrable Case of Kozlov-treshchev Birkhoff Integrable Potentials

The integrability of this system was conjectured in [16] and in the book of V.V. Kozlov [17]. This system appears first in the classification of Birkhoff integrable systems by Kozlov and Treshchev [16]. The classification involves systems with exponential interraction with sufficient number of integrals, polynomial in the momenta. The classification gives necessary conditions for a system with ...

Quasi-Exactly Solvable Time-Dependent Potentials

We find exact solutions of the time-dependent Schrödinger equation for a family of quasiexactly solvable time-dependent potentials by means of non-unitary gauge transformations. PACS numbers: 03.65.Ge, 11.30.Na, 03.65.Fd (∗) Research supported by DCGICYT Grant # PB95-0401. (∗∗) Research supported by NSERC Grant # 0GP0105490, on sabbatical leave from the Department of Mathematics and Statistics,...

Polymer dynamics in time-dependent periodic potentials.

The dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary-state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we ...

Solitary wave dynamics in time-dependent potentials

We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schrödinger equation in time-dependent external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schrödinger equation. We then show that when the external potential varies slowly in space compared to the size of the soliton, th...