Journal of Nonlinear Mathematical Physics

Volume 13, Issue 2, May 2006

1. Note on the evolution of compactly supported initial data under the Camassa-Holm flow

Enrique LOUBET
Pages: 158 - 162
We clarify and extend some remarks raised in [5] [Constantin A, J. Math. Phys. 46 (2005), 023506] about the evolution of compactly supported initial data under the Camassa-Holm flow.

2. Complex crystallographic Coxeter groups and affine root systems

Joseph BERNSTEIN, Ossip SCHWARZMAN
Pages: 163 - 182
We classify (up to an isomorphism in the category of affine groups) the complex crystallographic groups generated by reflections and such that d, its linear part, is a Coxeter group, i.e., d is generated by "real" reflections of order 2.

4. The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources

Ting XIAO, Yunbo ZENG
Pages: 193 - 204
For the first time we show that the quasiclassical limit of the symmetry constraint of the Sato operator for the KP hierarchy leads to the generalized Zakharov reduction of the Sato function for the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the...

5. New Cellular Automata associated with the Schroedinger Discrete Spectral Problem

M BRUSCHI
Pages: 205 - 210
New Cellular Automata associated with the Schroedinger discrete spectral problem are derived. These Cellular Automata possess an infinite (countable) set of constants of motion.

6. Application of Lie group analysis to a core group model for sexually transmitted diseases

M EDWARDS, M C NUCCI
Pages: 211 - 230
Lie group analysis is applied to a core group model for sexually transmitted disease formulated by Hadeler and Castillo-Chavez [Hadeler K P and Castillo-Chavez C, A core group model for disease transmission, Math. Biosci. 128 (1995), 41­55]. Several instances of integrability even linearity are found...

7. New solvable many-body problems in the plane

F CALOGERO, J-P FRANCOISE
Pages: 231 - 254
We revisit an integrable (indeed, superintegrable and solvable) many-body model itroduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model...

8. Boundary conditions and Conserved densities for potential Zabolotskaya-Khokhlov equation

V ROSENHAUS
Pages: 255 - 270
We study local conservation laws and corresponding boundary conditions for the ptential Zabolotskaya-Khokhlov equation in (3+1)-dimensional case. We analyze an infinite Lie point symmetry group of the equation, and generate a finite number of conserved quantities corresponding to infinite symmetries...

9. Massless Pseudo-scalar Fields and Solution of the Federbush Model

S E KORENBLIT, V V SEMENOV
Pages: 271 - 284
The formal Heisenberg equations of the Federbush model are linearized and then are directly integrated applying the method of dynamical mappings. The fundamental role of two-dimensional free massless pseudo-scalar fields is revealed for this procedure together with their locality condition taken into...

10. Symmetries and invariants for the 2D-Ricci flow model

Rodica CIMPOIASU, Radu CONSTANTINESCU
Pages: 285 - 292
The paper investigates some special Lie type symmetries and associated invariant quantities which appear in the case of the 2D Ricci flow equation in conformal gauge. Starting from the invariants some simple classes of solutions will be determined.

11. Interpolation of entire functions, product formula for basic sine function

Fethi BOUZEFFOUR
Pages: 293 - 301
We solve the problem of constructing entire functions where ln M(r; f) grows like ln2 r from their values at q-n , for 0 < q < 1. As application we give a product formula for the basic sine function.

12. Hamiltonian formalism of the Landau-Lifschitz equation for a spin chain with full anisotropy

Nian-Ning HUANG, Hao CAI, Tian YAN, Fan-Rong XU
Pages: 302 - 314
The Hamiltonian formalism of the Landau-Lifschitz equation for a spin chain with full anisotropy is formulated completely, which constructs a stable base for further investigations.