Algebro-geometric solutions of the Harry Dym equation

DOI10.1007/BF02674299zbMath0921.58028MaRDI QIDQ1288101

D. P. Novikov

Publication date: 10 May 1999

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

nonlinear equationsolitonintegrable systemfinite-gap solutionsHarry Dym equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (14)

Elliptic equation's new solutions and their applications to two nonlinear partial differential equations ⋮ Solving the Dym initial value problem in reproducing kernel space ⋮ Algebro-geometric solutions of the Harry Dym hierarchy ⋮ New rational solitary wave solutions of \((2+1)\)-dimensional Burgers equation ⋮ Bounded traveling wave solutions and their relations for the generalized HD type equation ⋮ Quasi-periodic wave solutions for the \((2+1)\)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (CBS) equation ⋮ A new integrable equation with peakons and cuspons and its bi-Hamiltonian structure ⋮ Method for constructing analytical solutions to the Dym initial value problem ⋮ The novel solutions of auxiliary equation and their application to the \((2 + 1)\)-dimensional Burgers equations ⋮ Symbolic computation and non-travelling wave solutions of \((2 + 1)\)-dimensional nonlinear evolution equations ⋮ Some exact and new solutions of the Nizhnik-Novikov-Vesselov equation using the Exp-function method ⋮ A two-component generalization of Burgers' equation with quasi-periodic solution ⋮ On the nontrivial non-travelling wave profiles of nonlinear evolution and wave equations ⋮ Long time behavior and soliton solution for the Harry Dym equation

Cites Work

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• Explicit algebraic description of hyperelliptic Jacobians on the basis of the Klein \(\sigma\)-functions
• The Harry Dym equation on the complex plane: Inverse spectral transform and exact solutions
• 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 higher-times approach to multisoliton solutions of the Harry Dym equation
• The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
• delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation
• On some spectral problems and isospectral evolutions connected with the classical string problem

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