Journal of Nonlinear Mathematical Physics

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.

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.

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 dKP...

New Cellular Automata associated with the Schroedinger discrete spectral problem are derived. These Cellular Automata possess an infinite (countable) set of constants of motion.

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...

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...

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...

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...

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.

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

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.