BookDOI
The nonlinear Schrödinger equation : self-focusing and wave collapse
TLDR
In this article, the authors present a basic framework to understand structural properties and long-time behavior of standing wave solutions and their relationship to a mean field generation and acoustic wave coupling.Abstract:
Basic Framework.- The Physical Context.- Structural Properties.- Rigorous Theory.- Existence and Long-Time Behavior.- Standing Wave Solutions.- Blowup Solutions.- Asymptotic Analysis near Collapse.- Numerical Observations.- Supercritical Collapse.- Critical Collapse.- Perturbations of Focusing NLS.- Coupling to a Mean Field.- Mean Field Generation.- Gravity-Capillary Surface Waves.- The Davey-Stewartson System.- Coupling to Acoustic Waves.- Langmuir Oscillations.- The Scalar Model.- Progressive Waves in Plasmas.read more
Citations
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Journal ArticleDOI
Localized chaotic patterns in weakly dissipative systems
TL;DR: In this paper, a new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found.
Journal ArticleDOI
Cascades in nonlocal turbulence.
TL;DR: The exact flux constancy laws are derived, analogs of Kolmogorov's 4/5 law for incompressible fluid turbulence, expressed via the fourth-order moment and valid for any nonlinearity.
Journal ArticleDOI
Variational analysis of anisotropic Schrödinger equations without Ambrosetti–Rabinowitz-type condition
TL;DR: In this paper, weak solutions to nonlinear stationary Schrodinger-type equations of the form (i.e., √ √ n = 1/n √ N √ partial √ x_i,x_i) are analyzed.
Journal ArticleDOI
Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves
Agissilaos Athanassoulis,Gerassimos A. Athanassoulis,Gerassimos A. Athanassoulis,Themistoklis P. Sapsis +3 more
TL;DR: In this paper, the Wigner transform and the Penrose condition are used to recover spatially periodic unstable wave modes, which are called unstable Penrose modes, and their parameters are obtained by resolving the penrose condition, a system of nonlinear equations involving P(k).
Journal ArticleDOI
Computing multiple peak solutions for Bose–Einstein condensates in optical lattices
S.-L. Chang,C.-S. Chien +1 more
TL;DR: Numerical results show that the number of peaks for the ground state solutions of BEC in a periodic potential depends on the distance of neighbor wells, and also investigate multiple peak solutions for BEC confined in optical lattices.