arXiv subjects
Publications and source records attributed to Jose Carlos Brunelli.
We show how the Yao-Zeng system of coupled short-pulse equations is related to the original short-pulse equation and obtain the correct zero-curvature representation of the Yao-Zeng system via this relationship.
We provide a geometrical interpretation for the series of transformations used by Sakovich to map the third-order nonlinear evolution equation obtained by Chou and Qu to the mKdV equation. We also discuss its bi-Hamiltonian integrability as well as integrable equations associated with this system.
We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.
We study a new hierarchy of equations containing the Short Pulse equation, which describes the evolution of very short pulses in nonlinear media, and the Elastic Beam equation, which describes nonlinear transverse oscillations of elastic beams under tension. We show that the hierarchy of equations is integrable. We obtain the two compatible Hamiltonian structures. We construct an infinite series of both local and nonlocal conserved charges. A Lax description is presented for both systems. For the Elastic Beam equations we also obtain a nonstandard Lax representation.
We prove the integrability of the short pulse equation derived recently by Schäfer and Wayne from a hamiltonian point of view. We give its bi-hamiltonian structure and show how the recursion operator defined by the hamiltonian operators is connected with the one obtained by Sakovich and Sakovich. An alternative zero-curvature formulation is also given.
Computer algebra procedures to manipulate pseudo-differential operators are implemented to perform calculations with integrable models. We use lazy evaluation and streams to represent and operate with pseudo-differential operators. No order of truncation is needed since terms are produced on demand. We give a series of concrete examples using the computer algebra language MAPLE.