Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

Giacomo Roberti; Gennady El; Alexander Tovbis; François Copie; Pierre Suret; Stéphane Randoux

doi:10.1103/PhysRevE.103.042205

Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

Giacomo Roberti, Gennady El, Alexander Tovbis, François Copie, Pierre Suret, Stéphane Randoux^*

^*Corresponding author for this work

Mathematics, Physics and Electrical Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We numerically realize a breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial"generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207].

Original language	English
Article number	042205
Pages (from-to)	1-13
Number of pages	13
Journal	Physical Review E
Volume	103
Issue number	4
Early online date	9 Apr 2021
DOIs	https://doi.org/10.1103/PhysRevE.103.042205
Publication status	Published - Apr 2021

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10.1103/PhysRevE.103.042205

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title = "Numerical spectral synthesis of breather gas for the focusing nonlinear Schr{\"o}dinger equation",

abstract = "We numerically realize a breather gas for the focusing nonlinear Schr{\"o}dinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a {"}trial{"}generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207]. ",

author = "Giacomo Roberti and Gennady El and Alexander Tovbis and Fran{\c c}ois Copie and Pierre Suret and St{\'e}phane Randoux",

note = "Funding Information: This work was partially supported by the Agence Nationale de la Recherche through the I-SITE ULNE (Grant No. ANR-16-IDEX-0004), the LABEX CEMPI (Grant No. ANR-11- LABX-0007), and the Equipex Flux (Grant No. ANR-11-EQPX- 0017), as well as by the Ministry of Higher Education and Research, Hauts de France Council and European Regional Development Fund through the CPER project Photonics for Society (P4S), EPSRC (UK) Grant No. EP/R00515X/2 (G.E.), US NSF Grant No. DMS 2009647 (A.T.), and Dstl (UK) Grant No. DSTLX-1000116851 (G.R., G.E., and S.R.). G.E., A.T., and G.R. thank the PhLAM laboratory at the University of Lille for hospitality and partial financial support.",

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AU - Roberti, Giacomo

AU - El, Gennady

AU - Tovbis, Alexander

AU - Copie, François

AU - Suret, Pierre

AU - Randoux, Stéphane

N1 - Funding Information: This work was partially supported by the Agence Nationale de la Recherche through the I-SITE ULNE (Grant No. ANR-16-IDEX-0004), the LABEX CEMPI (Grant No. ANR-11- LABX-0007), and the Equipex Flux (Grant No. ANR-11-EQPX- 0017), as well as by the Ministry of Higher Education and Research, Hauts de France Council and European Regional Development Fund through the CPER project Photonics for Society (P4S), EPSRC (UK) Grant No. EP/R00515X/2 (G.E.), US NSF Grant No. DMS 2009647 (A.T.), and Dstl (UK) Grant No. DSTLX-1000116851 (G.R., G.E., and S.R.). G.E., A.T., and G.R. thank the PhLAM laboratory at the University of Lille for hospitality and partial financial support.

PY - 2021/4

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N2 - We numerically realize a breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial"generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207].

AB - We numerically realize a breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial"generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207].

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Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

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