The Harry Dym equation on the complex plane: Inverse spectral transform and exact solutions

DOI10.1007/BF01016150zbMath0850.35088MaRDI QIDQ1918831

Jyh-Hao Lee, B. G. Konopelchenko

Publication date: 18 November 1996

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

zbMATH Keywords

essential singularityHarry Dym equationinverse spectral transform\(\overline\partial\)-dressing method\(\overline\partial\)-method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51)

Related Items (4)

Algebro-geometric solutions of the Harry Dym hierarchy ⋮ Dirichlet series and the integrability of multilinear differential equations ⋮ Algebro-geometric solutions of the Harry Dym equation ⋮ Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The dressing method and nonlocal Riemann-Hilbert problems
• Cusp Soliton of a New Integrable Nonlinear Evolution Equation
• Derivation and implicit solution of the Harry Dym equation and its connections with the Korteweg-de Vries equation
• The non-local delta problem and (2+1)-dimensional soliton equations
• Complex variable methods in Hele–Shaw moving boundary problems
• The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
• Linear spectral problems, non-linear equations and the δ-method
• On some spectral problems and isospectral evolutions connected with the classical string problem

This page was built for publication: The Harry Dym equation on the complex plane: Inverse spectral transform and exact solutions