169 research outputs found
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
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