Integrable boundary value problems for elliptic type Toda lattice in a disk

Download

index.pdf

Date

2007-10-01

Author

Guerses, Metin
Habibullin, Ismagil
Zheltukhın, Kostyantyn

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

140
views

0
downloads

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.

Subject Keywords

Mathematical Physics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/39615

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.2799256

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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...
EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN-GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-09-01) We present the exact solution of the Klein Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular ...
SYMMETRIC SPACE PROPERTY AND AN INVERSE SCATTERING FORMULATION OF THE SAS EINSTEIN-MAXWELL FIELD-EQUATIONS ERIS, A; GURSES, M; Karasu, Atalay (AIP Publishing, 1984-01-01) We formulate stationary axially symmetric (SAS) Einstein–Maxwell fields in the framework of harmonic mappings of Riemannian manifolds and show that the configuration space of the fields is a symmetric space. This result enables us to embed the configuration space into an eight‐dimensional flat manifold and formulate SAS Einstein–Maxwell fields as a σ‐model. We then give, in a coordinate free way, a Belinskii–Zakharov type of an inverse scattering transform technique for the field equations supplemented by a...
String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication Kondo, Satoshi; Watari, Taizan (Springer Science and Business Media LLC, 2019-04-01) It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Bo...
Gardner's deformations of the Boussinesq equations Karasu, Atalay (IOP Publishing, 2006-09-15) Using the algebraic method of Gardner's deformations for completely integrable systems, we construct recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these equations, we obtain new integrable systems adjoint with respect to the initial ones and describe their Hamiltonian structures and symmetry properties.

Citation Formats

M. Guerses, I. Habibullin, and K. Zheltukhın, “Integrable boundary value problems for elliptic type Toda lattice in a disk,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39615.