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• W2979490018 abstract "Solitons and breathers are localized solutions of integrable systems that can be viewed as particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media these integrable'' gases present fundamental interest for nonlinear physics. We develop analytical theory of breather and soliton gases by considering a special, thermodynamic type limit of the wavenumber-frequency relations for multi-phase (finite-gap) solutions of the focusing nonlinear Schrodinger equation. This limit is defined by the locus and the critical scaling of the band spectrum of the associated Zakharov-Shabat operator and yields the nonlinear dispersion relations for a spatially homogeneous breather or soliton gas, depending on the presence or absence of the background'' Stokes mode. The key quantity of interest is the density of states defining, in principle, all spectral and statistical properties of a soliton (breather) gas. The balance of terms in the nonlinear dispersion relations determines the nature of the gas: from an ideal gas of well separated, non-interacting breathers (solitons) to a special limiting state, which we term breather (soliton) condensate, and whose properties are entirely determined by the pairwise interactions between breathes (solitons). For a non-homogeneous breather gas, we derive a full set of kinetic equations describing slow evolution of the density of states and of its carrier wave counterpart. The kinetic equation for soliton gas is recovered by collapsing the Stokes spectral band. A number of concrete examples of breather and soliton gases are considered, demonstrating efficacy of the developed general theory with broad implications for nonlinear optics, superfluids and oceanography." @default.
• W2979490018 created "2019-10-18" @default.
• W2979490018 creator A5041019781 @default.
• W2979490018 creator A5067159581 @default.
• W2979490018 date "2020-05-08" @default.
• W2979490018 modified "2023-10-12" @default.
• W2979490018 title "Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation" @default.
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• W2979490018 doi "https://doi.org/10.1103/physreve.101.052207" @default.
• W2979490018 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/32575216" @default.
• W2979490018 hasPublicationYear "2020" @default.
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