turkmath.org

In the talk, we will consider a Hamiltonian system which describes a non-linear generalization of the shock-wave equation that is known to be integrable (Burgers-Hopf equations).The main result is an observation of the so-called Motzkin numbers in this Hamiltonian system, which usually appear in the description of lattice paths. Motzkin numbers appear as coefficients in integrals of motion thus rendering them precisely as Motzkin polynomials. The relationship of integrable models with lattice paths may be a new procedure in generating new dynamical systems.