Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas
Pierandrea Vergallo, E. V. Ferapontov
Abstract
We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing delta-functional reductions of the kinetic equation for dense soliton gas is established (for KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases).
Topics & Concepts
Hamiltonian (control theory)Degenerate energy levelsKorteweg–de Vries equationKinetic energyDegeneracy (biology)Mathematical physicsSolitonPhysicsSeparable spaceNonlinear systemHamiltonian systemMathematicsClassical mechanicsQuantum mechanicsMathematical analysisMathematical optimizationBioinformaticsBiologyCold Atom Physics and Bose-Einstein CondensatesGas Dynamics and Kinetic TheoryCatalysis and Oxidation Reactions