Real soliton lattices of the Kadomtsev-Petviashvili II equation and desingularization of spectral curves: the \(\mathrm{Gr}^{\mathrm{TP}}(2, 4)\) case

DOI10.1134/S0081543818060019zbMath1437.37086arXiv1803.10968OpenAlexW2907808561MaRDI QIDQ2280432

Simonetta Abenda, Petr G. Grinevich

Publication date: 18 December 2019

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10968

zbMATH Keywords

quasi-periodic solutionsKP-II equationrational M-curve

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relationships between algebraic curves and integrable systems (14H70) 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)

Related Items (7)

On reducible degeneration of hyperelliptic curves and soliton solutions ⋮ Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians ⋮ Reducible \(M\)-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons ⋮ Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation ⋮ The direct scattering problem for perturbed Kadomtsev–Petviashvili multi line solitons ⋮ Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk ⋮ Real regular KP divisors on \({\texttt{M}}\)-curves and totally non-negative Grassmannians

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