Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin's Integrability Classification of Perturbed KdV-Type Equations

Yarema A. Prykarpatskyy
2021 Symmetry  
Dubrovin's work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin's criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial
more » ... ynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.
doi:10.3390/sym13061077 fatcat:fc2erspbbbgjlm76vwsjhwikkq