On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known integrable systems: one--into a pair of decoupled KdV equations, the other one--into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page

On integrability of the Yao-Zeng two-component short-pulse equation

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.Comment: 5 page

Cyclic bases of zero-curvature representations: five illustrations to one concept

The paper contains five examples of using cyclic bases of zero-curvature representations in studies of weak and strong Lax pairs, hierarchies of evolution systems, and recursion operators.Comment: 18 page

Integrability of Kersten-Krasil'shchik coupled KdV-mKdV equations: singularity analysis and Lax pair

The integrability of a coupled KdV-mKdV system is tested by means of singularity analysis. The true Lax pair associated with this system is obtained by the use of prolongation technique.Comment: 9 page

Hamiltonian Structures for the Ostrovsky-Vakhnenko Equation

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.Comment: 13 page

A strange recursion operator for a new integrable system of coupled Korteweg - de Vries equations

A recursion operator is constructed for a new integrable system of coupled Korteweg - de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is characterized by unusual structure of its nonlocal part.Comment: 12 pages, final versio