Liouville Correspondences between Integrable Hierarchies
Copyright policy )Liouville Correspondences between Integrable Hierarchies
In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada-Kotera equations, and the isospectral problems of the Degasperis-Procesi and Kaup-Kupershmidt equations relate the corresponding hierarchies, in both positive and negative directions, as well as their associated conservation laws. Combining these results with the Miura transformation relating the Sawada-Kotera and Kaup-Kupershmidt equations, we further construct an implicit relationship which associates the Novikov and Degasperis-Procesi equations.
- University of Minnesota Morris United States
- North University of China China (People's Republic of)
- Ningbo University China (People's Republic of)
Sawada-Kotera equation, Kaup-Kupershmidt equation, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Liouville transformation, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, bi-Hamiltonian structure, Degasperis-Procesi equation, conservation law, Novikov equation, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Miura transformation
Sawada-Kotera equation, Kaup-Kupershmidt equation, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Liouville transformation, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, bi-Hamiltonian structure, Degasperis-Procesi equation, conservation law, Novikov equation, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Miura transformation
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