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The General Solution of the Complex Monge-Amp\`ere Equation in two
dimensional space | The general solution to the Complex Monge-Amp\`ere equation in a two
dimensional space is constructed.
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The Complex Bateman Equation in a space of arbitrary dimension | A general solution to the Complex Bateman equation in a space of arbitrary
dimensions is constructed.
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The General Solution of the Complex Monge-Amp\`ere Equation in a space
of arbitrary dimension | A general solution to the Complex Monge-Amp\`ere equation in a space of
arbitrary dimensions is constructed.
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Darboux Transformation for Supersymmetric KP Hierarchies | We construct Darboux transformations for the super-symmetric KP hierarchies
of Manin--Radul and Jacobian types. We also consider the binary Darboux
transformation for the hierarchies. The iterations of both type of Darboux
transformations are briefly discussed.
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Darboux transformations for a Bogoyavlenskii equation in 2+1 dimensions | We use the singular manifold method to obtain the Lax pair, Darboux
transformations and soliton solutions for a (2+1) dimensional integrable
equation.
|
The Structure of the Bazhanov-Baxter Model and a New Solution of the
Tetrahedron Equation | We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state
integrable model. There are two essential points, i) the cubic symmetries, and
ii) the spherical trigonometry parametrization, to understand the structure of
this model. We propose two approaches to find a candidate as a solution of the
tetrahedron equation, and we find a new solution.
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Orthogonal and symplectic matrix integrals and coupled KP hierarchy | Orthogonal and symplectic matrix integrals are investigated. It is shown that
the matrix integrals can be considered as a $\tau$-function of the coupled KP
hierarchy, whose solution can be expressed in terms of pfaffians.
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Dressing method and the coupled KP hierarchy | The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by
using the dressing method. It is shown that the coupled KP hierarchy can be
reformulated as a reduced case of the 2-component KP hierarchy.
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Matrix integrals and the geometry of spinors | We obtain the collection of symmetric and symplectic matrix integrals and the
collection of Pfaffian tau-functions, recently described by Peng and Adler and
van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector
of a fermionic Fock space. This fermionic Fock space is the same space as one
constructs to obtain the KP and 1-Toda lattice hierarchy.
|
Dispersionless Fermionic KdV | We analyze the dispersionless limits of the Kupershmidt equation, the SUSY
KdV-B equation and the SUSY KdV equation. We present the Lax description for
each of these models and bring out various properties associated with them as
well as discuss open questions that need to be addressed in connection with
these models.
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The KdV equation on a half-line | The initial boundary value problem on a half-line for the KdV equation with
the boundary conditions $u|_{x=0}=a\leq0$, $u_{xx}|_{x=0}=3a^2$ is integrated
by means of the inverse scattering method. In order to find the time evolution
of the scattering matrix it turned out to be sufficient to solve the Riemann
problem on a hyperelliptic curve of genus two, where the conjugation matrices
are effectively defined by initial data.
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Lax pair, Darboux Transformations and solitonic solutions for a (2+1)
dimensional NLSE | In this paper the Singular Manifold Method has allowed us to obtain the Lax
pair, Darboux transformations and tau functions for a non-linear Schr\"odiger
equation in 2+1 dimensions. In this way we can iteratively build different kind
of solutions with solitonic behavior.
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Exact Solution of the Quantum Calogero-Gaudin System and of its
q-Deformation | A complete set of commuting observables for the Calogero-Gaudin system is
diagonalized, and the explicit form of the corresponding eigenvalues and
eigenfunctions is derived. We use a purely algebraic procedure exploiting the
co-algebra invariance of the model; with the proper technical modifications
this procedure can be applied to the $q-$deformed version of the model, which
is then also exactly solved.
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Schlesinger transformations for elliptic isomonodromic deformations | Schlesinger transformations are discrete monodromy preserving symmetry
transformations of the classical Schlesinger system. Generalizing well-known
results from the Riemann sphere we construct these transformations for
isomonodromic deformations on genus one Riemann surfaces. Their action on the
system's tau-function is computed and we obtain an explicit expression for the
ratio of the old and the transformed tau-function.
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Form factors of the SU(2) invariant massive Thirring model with boundary
reflection | The SU(2) invariant massive Thirring model with a boundary is considered on
the basis of the vertex operator approach. The bosonic formulae are presented
for the vacuum vector and its dual in the presence of the boundary. The
integral representations are also given for form factors of the present model.
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Canonical transformations of the time for the Toda lattice and the Holt
system | For 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 change of the time. On the other hand,
mapping of the time induces transformations of the action-angles variables and
a shift of the generating function of the B\"{a}cklund transformation.
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Introduction to the functions on compact Riemann surfaces and
theta-functions | We 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 from topology and complex
analysis. the treatment is organized to give a background for further
applications to non-linear differential equations.
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Bicomplexes and finite Toda lattices | We 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.
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Quantum Lax scheme for Ruijsenaars models | We 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 method generalized to the case of face
Hopf algebras and elliptic quantum groups with dynamical R-matrices.
|
Group Theoretical Properties and Band Structure of the Lame Hamiltonian | We 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 symmetry limits.
|
Quantum Lax Pair From Yang-Baxter Equations | We 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 boundary terms.
|
Liouville equation under perturbation | Small 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.
|
Whitham-Toda Hierarchy in the Laplacian Growth Problem | The 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 harmonic moments of the growing
domain. The Laplacian growth equation itself is the quasiclassical version of
the string equation that selects the solution to the hierarchy.
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Singular solution of the Liouville equation under perturbation | Small 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 one. The main object is an
asymptotics of the singular lines.
|
On the Miura map between the dispersionless KP and dispersionless
modified KP hierarchies | 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. Moreover, inspired by the works of Takasaki
and Takebe, the twistor construction of solution structure for the
dispersionless modified KP hierarchy is given.
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Spin Dynamics of La_2CuO_4 and the Two-Dimensional Heisenberg Model | The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate
$1/T_{2G}$ for the 2D Heisenberg model are calculated using quantum Monte Carlo
and maximum entropy analytic continuation. The results are compared to recent
experiments on La$_2$CuO$_4$, as well as predictions based on the non-linear
$\sigma$-model.
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Two-hole bound states in modified t-J model | We consider modified $t-J$ model with minimum of single-hole dispersion at
the points $(0,\pm \pi)$, $(\pm \pi,0)$. It is shown that two holes on
antiferromagnetic background produce a bound state which properties strongly
differs from the states known in the unmodified $t-J$ model. The bound state is
d-wave, it has four nodes on the face of the magnetic Brillouin zone. However,
in the coordinate representation it looks like as usual s-wave.
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Superconducting, magnetic, and charge correlations in the doped
two-chain Hubbard model | Superconducting, magnetic, and charge correlation functions and dynamic spin
correlation functions of the doped two-chain Hubbard model is studied with the
projector Quantum Monte carlo method and Lanczos recursion method. Of the three
correlation functions, the interchain singlet superconducting correlation
function is the most long range. Our data is not consistent with the
Luther-Emery picture.
|
The Bean Critical State: Infinitely Unstable | The threshold for creep in the Bean critical state is investigated. We
perturb the Bean state by an energy $\Delta\epsilon$. We find that no matter
how small $\Delta\epsilon$ is it will always be able to induce creep somewhere
on the Bean profile. This finding has important consequences for the
interpretation of low temperature creep phenomena in terms of quantum creep.
|
S-35 Beta Irradiation of a Tin Strip in a State of Superconducting
Geometrical Metastability | We report the first energy loss spectrum obtained with a geometrically
metastable type I superconducting tin strip irradiated by the beta-emission of
S-35. (Nucl. Instr. Meth. A, in press)
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Coupling of Josephson flux-flow oscillators to an external RC load | We investigate by numerical simulations the behavior of the power dissipated
in a resistive load capacitively coupled to a Josephson flux flow oscillator
and compare the results to those obtained for a d.c. coupled purely resistive
load. Assuming realistic values for the parameters R and C, both in the high-
and in the low-Tc case the power is large enough to allow the operation of such
a device in applications.
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On Mean-Field Theory of Quantum Phase Transition in Granular
Superconductors | In previous work on quantum phase transition in granular superconductors,
where mean-field theory was used, an assumption was made that the order
parameter as a function of the mean field is a convex up function. Though this
is not always the case in phase transitions, this assumption must be verified,
what is done in this article.
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Flux flow resistivity and vortex viscosity of high-Tc films | The flux flow regime of high-T$_{\rm c}$ samples of different normal state
resistivities is studied in the temperature range where the sign of the Hall
effect is reversed. The scaling of the vortex viscosity with normal state
resistivity is consistent with the Bardeen-Stephen theory. Estimates of the
influence of possible mechanisms suggested for the sign reversal of the Hall
effect are also given.
|
Evidence for Quasiparticle Decay in Photoemission from Underdoped
Cuprates | I argue that the ``gap'' recently observed at the Brillouin zone face of
cuprate superconductors in photoemission by Marshall et al [Phys. Rev. Lett.
76, 4841 (1996)] and Ding et al [Nature 382, 54 (1996)] is evidence for the
decay of the injected hole into a spinon-holon pair.
|