Journal of Nonlinear Mathematical Physics

Volume 12, Issue 4, November 2005

1. Seiberg-Witten-like Equations on 7-Manifolds

Nedim DEGIRMENCI, Nülifer ÖZDEMIR
Pages: 457 - 461
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.

2. On the Integrability of a Class of Nonlinear Dispersive Wave Equations

Ivanov ROSSEN
Pages: 462 - 468
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.

3. Bernoulli Numbers and Solitons

Marie-Pierre GROSSET, Alexander P VESELOV
Pages: 469 - 474
We present a new formula for the Bernoulli numbers as the following integral B2m = (-1)m-1 22m+1 +( dm-1 dxm-1 sech2 x)2 dx. 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...

4. Box-Ball System with Reflecting End

Atsuo KUNIBA, Masato OKADO, Yasuhiko YAMADA
Pages: 475 - 507
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...

5. Equations Of Long Waves With A Free Surface III. The Multidimensional Case

Boris A KUPERSHMIDT
Pages: 508 - 517
Long-wave equations for an incompressible inviscid free-surface fluid in N + 1 dimesions are derived and shown to be Hamiltonian and liftable into the space of moments.

6. The Asymptotic Behavior of the Solution of Boundary Value Problems for the sine-Gordon Equation on a Finite Interval

Beatrice PELLONI
Pages: 518 - 529
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...

7. Laplacians on Lattices

Wojtek J ZAKRZEWSKI
Pages: 530 - 538
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) and (2)Z...

8. On A Group Of Automorphisms Of The Noncommutative Burgers Hierarchy

Boris A KUPERSHMIDT
Pages: 539 - 549
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.

9. Asymptotic Scaling in a Model Class of Anomalous Reaction-Diffusion Equations

Giuseppe GAETA, Rosaria MANCINELLI
Pages: 550 - 566
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...

10. Classification of Fully Nonlinear Integrable Evolution Equations of Third Order

Rafael HERNANDEZ HEREDERO
Pages: 567 - 585
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...

11. Asymptotic Approximations in Quantum Calculus

Ahmed FITOUHI, Kamel BRAHIM, Néji BETTAIBI
Pages: 586 - 606
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...