On the discretization of Darboux Integrable Systems

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.


On the dynamics of singular continuous systems
Güler, Y (1989-04-01)
The Hamilton–Jacobi theory of a special type of singular continuous systems is investigated by the equivalent Lagrangians method. The Hamiltonian is constructed in such a way that the constraint equations are involved in the canonical equations implicitly. The Hamilton–Jacobi partial differential equation is set up in a similar manner to the regular case
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...
The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems
Leach, PGL; Karasu, Emine Ayşe (Informa UK Limited, 2004-05-01)
A recent paper by Karasu (Kalkanli) and Yildirim (Journal of Nonlinear Mathematical Physics 9 (2002) 475-482) presented a study of the Kepler-Ermakov system in the context of determining the form of an arbitrary function in the system which was compatible with the presence of the sl(2, R) algebra characteristic of Ermakov systems and the existence of a Lagrangian for a subset of the systems. We supplement that analysis by correcting some results.
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
K. Zheltukhın, “On the discretization of Darboux Integrable Systems,” JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, pp. 616–632, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46949.