Keyword search (4,164 papers available)

"Bertola M" Authored Publications:

Title Authors PubMed ID
1 Exactly Solvable Anharmonic Oscillator, Degenerate Orthogonal Polynomials and Painlevé II Bertola M; Chavez-Heredia E; Grava T; 38983592
MATHSTATS
2 Soliton Shielding of the Focusing Nonlinear Schrödinger Equation Bertola M; Grava T; Orsatti G; 37027854
CONCORDIA
3 Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach Bertola M; Blackstone E; Katsevich A; Tovbis A; 32684912
MATHSTATS
4 Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation. Tikan A, Billet C, El G, Tovbis A, Bertola M, Sylvestre T, Gustave F, Randoux S, Genty G, Suret P, Dudley JM 28777604
PHYSICS

 

Title:Soliton Shielding of the Focusing Nonlinear Schrödinger Equation
Authors:Bertola MGrava TOrsatti G
Link:https://pubmed.ncbi.nlm.nih.gov/37027854/
DOI:10.1103/PhysRevLett.130.127201
Publication:Physical review letters
Keywords:
PMID:37027854 Category: Date Added:2023-04-07
Dept Affiliation: CONCORDIA
1 SISSA, via Bonomea 265, 34136, Trieste, Italy.
2 Concordia University, 1455 Avenue de Maisonneuve W. 1455 Avenue de Maisonneuve West, H4G 1M8, Montréal, Canada.
3 INFN, Sezione di Trieste, via Valerio 2, 34127, Trieste, Italy.
4 School of Mathematics, University of Bristol, Fry Building, Bristol, BS8 1UG, United Kingdom.

Description:

We first consider a deterministic gas of N solitons for the focusing nonlinear Schrödinger (FNLS) equation in the limit N?8 with a point spectrum chosen to interpolate a given spectral soliton density over a bounded domain of the complex spectral plane. We show that when the domain is a disk and the soliton density is an analytic function, then the corresponding deterministic soliton gas surprisingly yields the one-soliton solution with the point spectrum the center of the disk. We call this effect soliton shielding. We show that this behavior is robust and survives also for a stochastic soliton gas: indeed, when the N-soliton spectrum is chosen as random variables either uniformly distributed on the circle, or chosen according to the statistics of the eigenvalues of the Ginibre random matrix the phenomenon of soliton shielding persists in the limit N?8. When the domain is an ellipse, the soliton shielding reduces the spectral data to the soliton density concentrating between the foci of the ellipse. The physical solution is asymptotically steplike oscillatory, namely, the initial profile is a periodic elliptic function in the negative x direction while it vanishes exponentially fast in the opposite direction.





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