Stability problem in nonlinear wave propagation
An explicit expression for the excitation spectrum of the stationary solutions of a nonlinear wave equation is obtained. It is found that all branches of many-valued solutions of a nonlinear wave equation between the (2K+1,2K+2) turning points (branch points in the complex plane of the nonlinearity parameter) are unstable. Some parts of branches between the (2K,2K+1) turning points are also unstable. The instability of the latter is related to the possibility that pairs of complex conjugate eigenvalues cross the real axis in the κ plane.
KeywordsSpectroscopy State Physics Field Theory Elementary Particle Quantum Field Theory
Unable to display preview. Download preview PDF.
- 1.H. M. Gibbs, Optical Bistability: Controlling Light with Light, Academic Press, New York (1985).Google Scholar
- 3.H. M. Gibbs, G. Khitrova, and N. Peyghambarian, Nonlinear Photomics, Springe-Verlag Berlin-Heidelberg (1990).Google Scholar
- 4.A. C. Newell and J. V. Moloney, Nonlinear Optics, Addison-Wesley, Reading, MA (1992).Google Scholar
- 5.Yu. N. Ovchinnikov and I. M. Sigal, Preprint, University of Toronto (1997).Google Scholar