The Seiberg-Witten equations are of great importance in the study of topology of
smooth four-dimensional manifolds. In this work, we propose similar equations for
7-dimensional compact manifolds with G2-structure.
We investigate the integrability of a class of 1+1 dimensional models describing nolinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic
rods, shallow water waves, etc. The only completely integrable cases coincide with
the Camassa-Holm and Degasperis-Procesi equations.
We present a new formula for the Bernoulli numbers as the following integral
This formula is motivated by the results of Fairlie and Veselov, who discovered the
relation of Bernoulli polynomials with soliton theory.
Dedicated to Hermann Flaschka...
A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting
end is presented. It extends a box-ball system on an infinite lattice associated with
the crystal base of Uq(sln). A commuting family of time evolutions are obtained
by adapting the K matrices and the double...
In this article we use thve Fokas transform method to analyze boundary value prolems for the sine-Gordon equation posed on a finite interval. The representation of
the solution of this problem has already been derived using this transform method.
We interchange the role of the independent variables...
We consider some lattices and look at discrete Laplacians on these lattices. In partiular we look at solutions of the equation
(1) = (2)Z,
where (1) and (2) denote two such Laplacians on the same lattice. We show that,
in one dimension, when (i), i = 1, 2, denote
(1) = (i + 1) + (i - 1) - 2(i)
Bäcklund transformations are constructed for the noncommutative Burgers hierarchy,
generalizing the commutative ones of Weiss, Tabor, Carnevale, and Pickering. These
transformations are shown to be invertible and form a group.
We analyze asymptotic scaling properties of a model class of anomalous reactiodiffusion (ARD) equations. Numerical experiments show that solutions to these have,
for large t, well defined scaling properties. We suggest a general framework to anlyze asymptotic symmetry properties; this provides an analytical...
A fully nonlinear family of evolution equations is classified. Nine new integrable equtions are found, and all of them admit a differential substitution into the Korteweg-de
Vries or Krichever-Novikov equations. One of the equations contains hyperelliptic
functions, but it is transformable into the...
This paper aims to study the asymptotic approximation of some functions defined
by the q-Jackson integrals, for a fix q ]0, 1[. For this purpose, we shall attempt to
extend the classical methods by giving their q-analogues. In particular, a q-analogue
of the Watson's lemma is discussed and new asymptotic...