Primitive solutions of the Korteweg-de Vries equation

DOI10.1134/S0040577920030058zbMath1456.37071MaRDI QIDQ2193694

Patrik V. Nabelek, Vladimir E. Zakharov, Dmitry V. Zakharov, Sergey A. Dyachenko

Publication date: 20 August 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Korteweg-de Vries equationintegrable systemsoliton theoryinverse scattering problemprimitive solution

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) 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) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08)

Related Items (3)

On solutions to the nonlocal \(\overline{\partial}\)-problem and (2+1) dimensional completely integrable systems ⋮ Generalized primitive potentials ⋮ Algebro-geometric finite gap solutions to the Korteweg-de Vries equation as primitive solutions

Cites Work

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• Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics
• Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• Primitive potentials and bounded solutions of the KdV equation
• Non-periodic one-dimensional ideal conductors and integrable turbulence
• Inverse scattering on the line
• On symmetric primitive potentials

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