On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems*

DOI10.1088/1361-6544/ac20a5zbMath1479.31001arXiv2101.03964OpenAlexW3200090343MaRDI QIDQ5152131

Alexander Tovbis, Arno B. J. Kuijlaars

Publication date: 17 September 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.03964

zbMATH Keywords

integrable systemsSchrödinger equationKorteweg-de Vries equationGreen potentialsoliton gasminimising measure

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

Related Items (4)

Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation ⋮ Non-standard green energy problems in the complex plane ⋮ Soliton gas in integrable dispersive hydrodynamics ⋮ Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases

Cites Work

• A geometric viewpoint on generalized hydrodynamics
• The thermodynamic limit of the Whitham equations
• Primitive potentials and bounded solutions of the KdV equation
• Rigorous asymptotics of a KdV soliton gas
• Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves
• Partial differential equations. IX: Elliptic boundary value problems. Transl. from the Russian
• Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
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