The nonlinear Schrödinger equation : self-focusing and wave collapse

By Catherine Sulem, P. Sulem. 2004

1,690 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e11fd86309e8ef9e7b621650a364b6fa91e93704

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Global existence and compact attractors for the discrete nonlinear Schrödinger equation (2005, background): “See also the results of [12,32,41] for results on existence, stability and nonexistence of non-trivial standing waves, for the continuous and discrete NLS equations, respectively.”
Ill-posedness for nonlinear Schrodinger and wave equations (2003, background): “For s = sc, the same holds with c(t) independent of t.”
On sharp Strichartz inequalities in low dimensions (2006, methodology): “Later simplified proofs were given by Ginibre and Velo [4], see also [2, 11].”
Sharp Threshold for Blowup and Global Existence in Nonlinear Schrödinger Equations Under a Harmonic Potential (2005, background): “Especially the sharp thresholds for blowup and global existence are pursued strongly (see Dalfovo et al., 1999; Kagan et al., 1996, 1998; Sackett et al., 1999; Sulem and Sulem, 1999; Ueda and Leggett, 1998; Wadati and Tsurumi, 1998; Zhang, 1994, 2002).”
Asymptotic method of moving planes for fractional parabolic equations (2020, background): “For more details, one can see [5, 32, 41] and the references therein.”
A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation (2007, background): “The basic line of thought in the subject, motivated by heuristics (Soffer [24]), rigorous partial results (Tao [27, 28]), numerical simulation (Sulem-Sulem [ 26 ]), and analogy with the completely integrable one-dimensional case, is that a solution of (1.1) either completely disperses as t → ∞ (line”
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, background): “model in the latter case was also given in [23]. The equation has also been suggested as a model for rogue waves [58,20]. Further references on the physical aspect of the NLS equation can be found in [60,54]. Moreover, the NLS equation is also one of the prototypical inﬁnite-dimensional completely i”
The Stochastic Nonlinear Schrödinger Equation in H 1 (2003, background): “Also, blow-up phenomena are studied in the context of H 1 solutions (see Ref.([13])).”
Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term (2005, background): “The analysis we develop in this paper shows the key role played by the convection term |∇u|p.”
Solitary Wave Dynamics in an External Potential (2003, methodology): “Our approach is built on important developments in the nonlinear Schrödinger equation (NLS) in the last 20 years (see [11, 43] for reviews).”