We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times O(1/ε). The leading terms of the WKB solutions solve cubic Schrödinger equations. We show that the nonlinear normal form method of Joly, Métivier and Rauch [5] applies to this context. This implies that the Schröding...

For the semi-classical limit of the cubic, defocusing nonlinear Schrödinger equation with an external potential, we explain the notion of criticality before a caustic is formed. In the sub-critical and critical cases, we justify the WKB approximation. In the super-critical case, the WKB analysis provides a new phenomenon for the (classical) cubic, defocusing nonlinear Schrödinger equation, whic...

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lamé potential (derived from representations of a finite dimensional matrix expressed in terms of su(2) generators) with the results of the tight–binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lamé potential ...

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the We...

We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrödinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions keep a WKB structure, on a time interval independent of the Planck constant. We prove error estimates, which show that the quadratic observables can be comp...

A numerical technique is presented which yields an exact solution to the one-dimensional scattering problem. The algorithm is used to compute phase shift error curves associated with the WKB approximation. A variety of scattering potentials are considered and cover cases for which the WKB solution varies from extremely good to poor. It is shown that some commonly assumed forms for ionospheric e...

The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler-DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schroedinger-W...

We study the dynamics of a spherically symmetric dust shell separating two spacetime domains, the interior one being a part of the de Sitter spacetime and the exterior one having the extremal Reißner-Nordström geometry. Extending the ideas of previous works on the subject, we show that the it is possible to determine the (metastable) WKB quantum states of this gravitational system. PACS numbers...