The quantum dynamics of a simplest dissipative system, a particle moving in a constant external field , is exactly studied by taking into account its interaction with a bath of Ohmic spectral density. We apply the main idea and methods developed in our recent work [1] to quantum dissipative system with constant external field. Quantizing the dissipative system we obtain the simple and exact sol...

The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model then solutions always exist if the dissipation’s wave number dependence is super-linear. Below this critical power the dissipation appears to be insufficient. For instance, it is not known if the critical dissipative QG equation has global smooth ...

We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the trunca...

We shall study a special class of systems called dissipative systems. Intuitively, we can think of systems interacting with the surrounding via some input / output ports, exchanging power with the surrounding, storing some energy and dissipating some. For example, electrical systems exchange power with the surrounding via an inner product between the current and voltage, i.e., Pe = v i. Energy ...

In order to study the longtime behavior of a dissipative evolutionary equation, we generally aim to show that the dynamics of the equation is finite dimensional for long time. In fact, one possible way to express this fact is to prove that dynamical systems describing the evolutional equation comprise the existence of the global attractor 1 . The KDV equation without dissipative and forcing was...

We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids, also called generalized standard materials, the state of a material point is decribed by dissipative internal variables in addition to the elastic deformation and the temperature....

In this paper we explore connections between the underlying physics of dissipative systems and nonlinear robust control. In particular, we concentrate on the problem of stabilizing stationary solutions of nonlinear dissipative systems with states distributed in space. Dissipative systems are equipped with an entropy function which we employ to relate dissipation with the Hamilton-Jacobi-Bellman...

The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model then solutions always exist if the dissipation’s wave number dependence is super-linear. Below this critical power the dissipation appears to be insufficient. For instance, it is not known if the critical dissipative QG equation has global smooth ...

This paper deals with the dissipative problem for uncertain time-delay networked control systems with both multiple measurement and control packet dropouts. The uncertainty is assumed to satisfy a dissipative inequality, and the multiple measurement and control packet dropouts are described by two independent Bernoulli distributed sequences. By utilizing the Lyapunov functional method, a robust...