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

Variable Coefficient Third Order KdV Type of Equations

We show that the integrable subclassess of a class of third order non-autonomous equations are identical with the integrable subclassess of the autonomous ones.Comment: Latex file , 15 page

Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy

Recently proposed nonholonomic deformation of the KdV equation is solved through inverse scattering method by constructing AKNS-type Lax pair. Exact and explicit N-soliton solutions are found for the basic field and the deforming function showing an unusual accelerated (decelerated) motion. A two-fold integrable hierarchy is revealed, one with usual higher order dispersion and the other with novel higher nonholonomic deformations.Comment: 7 pages, 2 figures, latex. Exact explicit exact N-soliton solutions (through ISM) for KdV field u and deforming function w are included. Version to be published in J. Phys.

A new integrable generalization of the Korteweg - de Vries equation

A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.Comment: 13 pages, 2 figure

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 general PDEs

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and Kupershmidt's deformation of a bi-Hamiltonian system.Comment: 12 pages; v2, v3: minor correction

Backlund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations

Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation from the trivial zero solution of this system.Comment: LaTeX, 5 page

Closed timelike curves and geodesics of Godel-type metrics

It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.Comment: REVTeX 4, 12 pages, no figures; the Introduction has been rewritten, some minor mistakes corrected, many references adde

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we provide an algebraic construction for the negative even mKdV hierarchy which gives rise to time evolutions associated to even graded Lie algebraic structure. We propose a modification of the dressing method, in order to incorporate a non-trivial vacuum configuration and construct a deformed vertex operator for $\hat{sl}(2)$, that enable us to obtain explicit and systematic solutions for the whole negative even grade equations