Liouville integrability conditions for monomial charge densities reduce to a negative Pell equation, generating an infinite set of commuting conserved charges for a new dispersionless Hamiltonian model.
Integrability properties of Motzkin polynomials
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abstract
We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable. Analyzing conserved currents of the system the letter shows, that these follow a nice pattern governed by coefficients of Motzkin polynomials, where each integral of motion corresponds to a path on a unit lattice.
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Arithmetic selection rules in dispersionless Hamiltonian systems
Liouville integrability conditions for monomial charge densities reduce to a negative Pell equation, generating an infinite set of commuting conserved charges for a new dispersionless Hamiltonian model.