Non-autonomous Svinolupov-Jordan KdV systems

Download
2001-07-20
Gurses, M
Karasu, Atalay
Turhan, R
Non-autonomous Svinolupov-Jordan KdV systems are considered. The integrability criteria of such systems are associated with the existence of recursion operators. A new non-autonomous KdV system and its recursion operator is obtained for all N. The examples for N = 2 and 3 are studied in detail. Some possible transformations which map some systems to autonomous ones are also discussed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

Suggestions

A class of nonautonomous coupled KdV systems
Turhan, R (AIP Publishing, 2004-02-01)
A class of nonautonomous coupled Korteweg-de Vries (KdV) systems in (1+1) dimensions are considered for integrability classification. Integrability of the systems is associated with the existence of a certain recursion operator. Some new integrable nonautonomous two-component KdV systems are found. (C) 2004 American Institute of Physics.
On the discretization of Darboux Integrable Systems
Zheltukhın, Kostyantyn (Informa UK Limited, 2020-10-01)
We study the discretization of Darboux integrable systems. The discretization is done using x-, y-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
Hydrodynamic type integrable equations on a segment and a half-line
Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2008-10-01)
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions in multifield systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semiline are presented. (C) 2008 American Institut...
Hamiltonian equations in R-3
Ay, Ahmet; GÜRSES, METİN; Zheltukhın, Kostyantyn (AIP Publishing, 2003-12-01)
The Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in R-3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the classification of irregular points and the corresponding reduced first order differential equations of several examples are given. (C) 2003 American Institute...
Integrability of Kersten-Krasil'shchik coupled KdV-mKdV equations: singularity analysis and Lax pair
Karasu, Emine Ayşe; Yurdusen, I (AIP Publishing, 2003-04-01)
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. (C) 2003 American Institute of Physics.
Citation Formats
M. Gurses, A. Karasu, and R. Turhan, “Non-autonomous Svinolupov-Jordan KdV systems,” JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, pp. 5705–5711, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46725.