39 research outputs found
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
Integrable Coupled KdV Systems
We give the conditions for a system of N- coupled Korteweg de Vries(KdV) type
of equations to be integrable. Recursion operators of each subclasses are also
given. All examples for N=2 are explicitly given.Comment: 17pp, LateX, to be published in J.Math.Phy
Gardner's deformations of the Boussinesq equations
Using the algebraic method of Gardner's deformations for completely
integrable systems, we construct the recurrence relations for densities of the
Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending
the Magri schemes for these systems, we obtain new integrable equations adjoint
with respect to the initial ones and describe their Hamiltonian structures and
symmetry properties.Comment: Proc. Workshop `Quantizaion, Dualities, and Integrable Systems,'
23-27 January 2006, Pamukkale University, Turkey; 7 pages. MSC 35Q53, 37K05,
37K10, 37K3
Non-autonomous Svinolupov Jordan KdV Systems
Non-autonomous Svinolupov-Jordan systems are considered. The integrability
criteria of such systems are associated with the existence of recursion
operators. A new non-autonomous KdV system is obtained and its recursion
operator is given for all . The examples for N=2 and N=3 are studied in
detail. Some possible transformations are also discussed which map some systems
to autonomous cases.Comment: Latex file (amssymb), 10 page
Minimal Extension of Einstein's Theory: The Quartic Gravity
We study structure of solutions of the recently constructed minimal
extensions of Einstein's gravity in four dimensions at the quartic curvature
level. The extended higher derivative theory, just like Einstein's gravity, has
only a massless spin-two graviton about its unique maximally symmetric vacuum.
The extended theory does not admit the Schwarzschild or Kerr metrics as exact
solutions, hence there is no issue of Schwarzschild type singularity but,
approximately, outside a source, spherically symmetric metric with the correct
Newtonian limit is recovered. We also show that for all Einstein space-times,
square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet
invariant) obeys a non-linear scalar Klein-Gordon equation.Comment: 12 pages, 2 figures, typos corrected, version to appear in PR
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
Higher Dimensional Metrics of Colliding Gravitational Plane Waves
We give a higher even dimensional extension of vacuum colliding gravitational
plane waves with the combinations of collinear and non-collinear polarized
four-dimensional metric. The singularity structure of space-time depends on the
parameters of the solution.Comment: 4 pages RevTex
Degenerate Svinolupov KdV systems
We find infinitely many coupled systems of KdV type equations which are integrable. We give also their recursion operators
On Construction of Recursion Operators From Lax Representation
In this work we develop a general procedure for constructing the recursion
operators fro non-linear integrable equations admitting Lax representation.
Svereal new examples are given. In particular we find the recursion operators
for some KdV-type of integrable equations.Comment: Latex File (AMS format), 23 pages, to be published in Journal of
Mathematical Physic
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