Integrability of Kersten-Krasil'shchik coupled KdV-mKdV equations: singularity analysis and Lax pair

Karasu, Emine Ayşe
Yurdusen, I
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.


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...
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar (AIP Publishing, 2010-06-01)
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
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...
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2009-03-01)
The point canonical transformation (PCT) approach is used to solve the Schrodinger equation for an arbitrary dimension D with a power-law position-dependent effective mass (PDEM) distribution function for the pseudoharmonic and modified Kratzer (Mie-type) diatomic molecular potentials. In mapping the transformed exactly solvable D-dimensional (D >= 2) Schrodinger equation with constant mass into the effective mass equation by using a proper transformation, the exact bound state solutions including the energ...
Integrable boundary value problems for elliptic type Toda lattice in a disk
Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2007-10-01)
The concept of integrable boundary value problems for soliton equations on R and R+ is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lattice and its reductions are found. (C) 2007 American Institute of Physics.
Citation Formats
E. A. Karasu and I. Yurdusen, “Integrability of Kersten-Krasil’shchik coupled KdV-mKdV equations: singularity analysis and Lax pair,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 1703–1708, 2003, Accessed: 00, 2020. [Online]. Available: