Backlund transformation and special solutions for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations

Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation from the trivial zero solution of this system.


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.
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...
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...
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...
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...
Citation Formats
E. A. Karasu, “Backlund transformation and special solutions for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations,” JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, pp. 7355–7358, 2001, Accessed: 00, 2020. [Online]. Available: