Soliton transverse instabilities in nonlocal nonlinear media

We analyze the transverse instabilities of spatial bright solitons in nonlocal nonlinear media, both analytically and numerically. We demonstrate that the nonlocal nonlinear response leads to a dramatic suppression of the transverse instability of the soliton stripes, and we derive the asymptotic expressions for the instability growth rate in both short- and long-wave approximations.Comment: 3 pages, 3 figure

Degeneracy of Landau Level and Quantum Group SL_q(2)

We show that there is a kind of quantum group symmetry $sl_{q}(2)$ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $sl_{q}(2)$.Comment: 10 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Director of Nankai Institute of Mathematics. Do not send emails to this computer accoun

WERE U.S. CROP YIELDS RANDOM IN RECENT YEARS?

Crop Production/Industries,

Crescent Waves in Optical Cavities

We theoretically and experimentally generate stationary crescent surface solitons pinged to the boundary of a micro-structured vertical cavity surface emission laser by using the intrinsic cavity mode as a background potential. Instead of a direct transition from linear to nonlinear cavity modes, we demonstrate the existence of a symmetry-breaking crescent waves without any analogs in the linear limit. Our results provide an alternative and general method to control lasing characteristics as well as to study optical surface waves.Comment: 3 figure