I Dimensions and Components.- General Introduction and Derivation of the DNLS Equation.- The One-Dimensional Case.- The Two-Dimensional Case.- The Three-Dimensional Case.- The Defocusing Case.-… Expand

We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form . This implies a corresponding (restricted) set of Strichartz estimates. Applications of… Expand

Basic Mean-Field Theory for Bose-Einstein Condensates.- Basic Mean-Field Theory for Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein… Expand

The solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations is proposed.Expand

An effective particle picture is developed and confirms that the deviation of the observed oscillation frequencies from the asymptotic prediction nu(z)/sqrt 2, where nu( z) is the longitudinal trapping frequency, results from the dimensionality of the system and the soliton interactions.Expand

We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Stationary soliton solutions of the nonlinear Dirac equation on simple… Expand