We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures.…
JCJen-Hsu Chang, Ming-Hsien Tu
Exactly Solvable and Integrable Systems papers
solv-intLatest research in Exactly Solvable and Integrable Systems
We discuss some algebraic aspects of the integrable vector non-linear Schr\"odinger hierarchies (GNLSr). These are hierarchies of zero-curvature equations constructed from affine Kac-Moody…
HBHarold BlasVertex operators, which are disguised Darboux maps, transform solutions of the KP equation into new ones. In this paper, we show that the bi-infinite sequence obtained by Darboux transforming an…
MAMark Adler, Pierre van MoerbekeSmall perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov…
LKL. A. KalyakinThe Laplacian growth problem in the limit of zero surface tension is proved to be equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy. The hierarchical times are…
MMMark Mineev-Weinstein, Anton ZabrodinSmall perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.
LKL. A. KalyakinReal forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
solv-intThree nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demonstrated that they possess a global…
OLOlaf Lechtenfeld, Alexander SorinWe show explicitly how to construct the quantum Lax pair for systems with open boundary conditions. We demonstrate the method by applying it to the Heisenberg XXZ model with general integrable…
ALA. Lima-SantosWe study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of bilinear identities,…
MAM. Adler, P. van MoerbekeWe show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using…
HLHui Li, Dimitri KusnezovWe study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical…
HLHui Li, Dimitri Kusnezov, Francesco IachelloAnalytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular…
LBL. V. Bogdanov, B. G. KonopelchenkoIntegrable Couplings of Soliton Equations by Perturbations I. A General Theory and Application to the KdV Hierarchy
solv-intA theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small…
WMWen-Xiu MaThe local Sugawara constructions of the "small" N=4 SCA in terms of supercurrents of N=2 extensions of the affinization of the sl(2|1) and sl(3) algebras are investigated. The associated super mKdV…
EIE. Ivanov, S. Krivonos, F. ToppanWe develop a quantum Lax scheme for IRF models and difference versions of Calogero-Moser-Sutherland models introduced by Ruijsenaars. The construction is in the spirit of the Adler-Kostant-Symes…
BJBranislav Jurco, Peter SchuppConstruction of variable mass sine-Gordon and other novel inhomogeneous quantum integrable models
solv-intThe inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact…
AKAnjan KunduWe study integrals of motion for Hirota bilinear difference equation that is satisfied by the eigenvalues of the transfer-matrix. The combinations of the eigenvalues of the transfer-matrix are found,…
APA. P. Protogenov, V. A. VerbusThe usual propetry of s<-->t duality for scattering amplitudes, e.g. for Veneziano amplitude, is deeply connected with the 2-dimensional geometry. In particular, a simple geometric construction of…
IKI. G. KorepanovBinary constrained flows of soliton equations admitting 2× 2 Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For…
YZYunbo Zeng, Wen-Xiu MaWe associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.
ADAristophanes Dimakis, Folkert Muller-HoissenA note on real forms of the complex N=4 supersymmetric Toda chain hierarchy in real N=2 and N=4 superspaces
solv-intThree inequivalent real forms of the complex N=4 supersymmetric Toda chain hierarchy (Nucl. Phys. B558 (1999) 545, solv-int/9907004) in the real N=2 superspace with one even and two odd real…
FDF. Delduc, A. SorinA family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions…
ABAngel Ballesteros, Francisco J. HerranzWe consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss…
CGCicogna GWe collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts…
DKD. KorotkinFor the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under…
ATAndrey Tsiganov