Spectrally Stable Encapsulated Vortices for Nonlinear Schr?dinger Equations |
| |
Authors: | Pego and Warchall |
| |
Institution: | (1) Department of Mathematics & Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA e-mail: rpego@ipst.umd.edu, US;(2) Department of Mathematics, University of North Texas, Denton, TX 76203, USA, US;(3) Division of Mathematical Sciences, National Science Foundation, USA, US |
| |
Abstract: | Summary. A large class of multidimensional nonlinear Schrodinger equations admit localized nonradial standing-wave solutions that
carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are spectrally
stable. We find such waves for equations in two space dimensions with focusing-defocusing nonlinearities, such as cubic-quintic. Spectrally stable waves resemble a vortex (nonlocalized solution with asymptotically
constant amplitude) cut off at large radius by a kink layer that exponentially localizes the solution.
For the evolution equations linearized about a localized spinning wave, we prove that unstable eigenvalues are zeroes of
Evans functions for a finite set of ordinary differential equations. Numerical computations indicate that there exist spectrally
stable standing waves having central vortex of any degree. |
| |
Keywords: | , solitary wave, stability, instability, multidimensional solitons, vortices, Evans function, saturable media, vortex,,,,,soliton, azimuthal modes, polydiacetylene para-toluene sulfonate |
本文献已被 SpringerLink 等数据库收录! |
|