416 research outputs found
Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
We show how to generate coupled KdV hierarchies from Staeckel separable
systems of Benenti type. We further show that solutions of these Staeckel
systems generate a large class of finite-gap and rational solutions of cKdV
hierarchies. Most of these solutions are new.Comment: 15 page
Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
Hamiltonian systems of hydrodynamic type occur in a wide range of
applications including fluid dynamics, the Whitham averaging procedure and the
theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the
integrability of such systems by the generalised hodograph transform implies
that integrable Hamiltonians depend on a certain number of arbitrary functions
of two variables. On the contrary, in 2+1 dimensions the requirement of the
integrability by the method of hydrodynamic reductions, which is a natural
analogue of the generalised hodograph transform in higher dimensions, leads to
finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we
classify integrable two-component Hamiltonian systems of hydrodynamic type for
all existing classes of differential-geometric Poisson brackets in 2D,
establishing a parametrisation of integrable Hamiltonians via
elliptic/hypergeometric functions. Our approach is based on the Godunov-type
representation of Hamiltonian systems, and utilises a novel construction of
Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page
Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models
New extra series of conserved densities for the polytropic gas model and
nonlinear elasticity equation are obtained without any references to the
recursion operator or to the Lax operator formalism. Our method based on the
utilization of the symmetry operators and allows us to obtain the densities of
arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics
behaviour are presented as an example. The special attention is paid for the
singular case for which we found new non homogenious solutions
expressed in terms of the elementary functions.Comment: 11 pages, 1 figur
Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are
investigated. The transformed operators are generally nonlocal, possessing a
number of remarkable algebraic and differential-geometric properties. We apply
our results to linearly degenerate semi-Hamiltonian systems in Riemann
invariants. Since all such systems are linearizable by appropriate
(generalized) reciprocal transformations, our formulae provide an infinity of
mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by
arbitrary functions of one variable.Comment: 26 page
Antibodies raised against a Sunn bug (Eurygaster integriceps Put.) recombinant protease, rGHP3p2, can inhibit gluten‐hydrolyzing activity
Sunn pest or Sunn bug, Eurygaster integriceps Put., salivary gland proteases are responsible for the deterioration of wheat flour quality during dough mixing, resulting from gluten hydrolysis. These proteases are highly heterogeneous and show low sensitivity to most types of proteinaceous inhibitors, meaning that such inhibitors cannot be used to prevent gluten damage. The present study describes the generation of a specific peptide antibody, raised against the active center of the recombinant gluten-hydrolyzing protease (GHP3). The recombinant protein, encoding two repeats of the GHP3 sequence element involved in forming the S4 pocket and binding of substrate at position P4, was designed and expressed in Escherichia coli. The antibodies raised to this recombinant protein showed inhibitory activity against the GHP3 protease. The results indicate that it is possible to design specific antibodies to inhibit wheat-bug gluten-hydrolyzing proteases
Hydrodynamic type integrable equations on a segment and a half-line
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 of multi-field 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 semi-line are presented
On the central quadric ansatz: integrable models and Painleve reductions
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley
(BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess
solutions whose level surfaces are central quadrics in the space of independent
variables (the so-called central quadric ansatz). It was demonstrated that
generic solutions of this type are described by Painleve equations PIII and
PII, respectively. The aim of our paper is threefold:
-- Based on the method of hydrodynamic reductions, we classify integrable
models possessing the central quadric ansatz. This leads to the five canonical
forms (including BF and dKP).
-- Applying the central quadric ansatz to each of the five canonical forms,
we obtain all Painleve equations PI - PVI, with PVI corresponding to the
generic case of our classification.
-- We argue that solutions coming from the central quadric ansatz constitute
a subclass of two-phase solutions provided by the method of hydrodynamic
reductions.Comment: 12 page
Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
We apply a version of the dressing method to a system of four dimensional
nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer
equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform
Method) and nonlinear matrix PDE integrable by the method of characteristics as
particular reductions. Some other reductions are suggested.Comment: 12 page
Lattice and q-difference Darboux-Zakharov-Manakov systems via -dressing method
A general scheme is proposed for introduction of lattice and q-difference
variables to integrable hierarchies in frame of -dressing
method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov
systems of equations are derived. Darboux, B\"acklund and Combescure
transformations and exact solutions for these systems are studied.Comment: 8 pages, LaTeX, to be published in J Phys A, Letters
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