22 research outputs found
On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators
We show that a recently introduced fifth-order bi-Hamiltonian equation with a
differentially constrained arbitrary function by A. de Sole, V.G. Kac and M.
Wakimoto is not a new one but a higher symmetry of a third-order equation. We
give an exhaustive list of cases of the arbitrary function in this equation, in
each of which the associated equation is inequivalent to the equations in the
remaining cases. The equations in each of the cases are linked to equations
known in the literature by invertible transformations. It is shown that the new
Hamiltonian operator of order seven, using which the introduced equation is
obtained, is trivially related to a known pair of fifth-order and third-order
compatible Hamiltonian operators. Using the so-called trivial compositions of
lower-order Hamiltonian operators, we give nonlocal generalizations of some
higher-order Hamiltonian operators
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
A new approach to the Lenard-Magri scheme of integrability
We develop a new approach to the Lenard-Magri scheme of integrability of
bi-Hamiltonian PDE's, when one of the Poisson structures is a strongly
skew-adjoint differential operator.Comment: 20 page
On integrability of some bi-Hamiltonian two field systems of PDE
We continue the study of integrability of bi-Hamiltonian systems with a
compatible pair of local Poisson structures (H_0,H_1), where H_0 is a strongly
skew-adjoint operator. This is applied to the construction of some new two
field integrable systems of PDE by taking the pair (H_0,H_1) in the family of
compatible Poisson structures that arose in the study of cohomology of moduli
spaces of curves.Comment: 30 page
A New Approach to the Lenard–Magri Scheme of Integrability
We develop a new approach to the Lenard–Magri scheme of integrability of bi-Hamiltonian PDEs, when one of the Poisson structures is a strongly skew-adjoint differential operator.Simons Foundation. Postdoctoral Fellowshi
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
Entegre edilebilir otonom olmayan KDV sistemler
Multi-component Korteweg-de Vries (KdV) type of nonautonomous systems in (1+1) dimensions are classified for integrability via existence of a recursion op erator having a certain general form. Integrability conditions are obtained for sys tems with arbitrary number of components. From these conditions two-component integrable systems are explicitly obtained. All the found integrable two-component nonautonomous systems are investigated for their transformability to autonomous systems.Çok bileşenli otonom olmayan (1+1) boyuttaki Korteweg-de Vries (KdV) tipi sistemlerin belirli bir genel formda simetri adım operatörünün varlığı üzerinden entegre edilebilirlik tasnifi yapıldı. Entegre edilebilme koşulları keyfi sayılardaki bileşenli sistemler için elde edildi. Bu koşullardan iki bileşenli entegre edilebilir sistemler açıkça bulundu. Bütün bulunan iki bileşenli otonom olmayan sistemler otonom sistemlere dönüşebilirlikleri açısından irdelendi.Ph.D. - Doctoral Progra