Integrability properties of Motzkin polynomials

Abstract

© 2020 Author(s). We consider a Hamiltonian system that has its origin in a generalization of the 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, this paper 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.