Lyapunov Stability of Ground States of Nonlinear Dispersive Evolution Equations,
PRINCETON UNIV NJ
Pagination or Media Count:
A solitary wave is a localized, finite energy solution of a nonlinear evolution equation. It results from a balance of dispersion and a focusing nonlinearity. Two fundamental equations in the theory of nonlinear waves that possess such solutions are the nonlinear Schrodinger equation NLS and the Korteweg deVries equation KdV. NLS arises in the mathematical description of electromagnetic wave propagation through nonlinear media. KdV arises in the study of waves in shallow water. This paper presents a new proof of orbital stability of ground state solitary waves of the nonlinear Schrodinger equation for a general class of nonlinearities. The stability of the solitary wave for the generalized Korteweg deVries equation is also shown.
- Numerical Mathematics