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The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives
- P. Kevrekidis
- 17 July 2009
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.-…
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations
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…
Emergent Nonlinear Phenomena in Bose-Einstein Condensates
Emergent nonlinear phenomena in Bose-Einstein condensates : theory and experiment
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…
The Discrete Nonlinear Schrödinger Equation
- P. Kevrekidis
Deciding the Nature of the Coarse Equation through Microscopic Simulations: The Baby-Bathwater Scheme
The solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations is proposed.
Experimental observation of oscillating and interacting matter wave dark solitons.
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.
Stability of discrete solitons in nonlinear Schrödinger lattices
Dynamics of Dirac solitons in networks
- K. Sabirov, D. Babajanov, D. Matrasulov, P. Kevrekidis
- PhysicsJournal of Physics A: Mathematical and…
- 20 January 2017
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…