Instability of standing waves for non-linear Schrödinger-type equations
- 10 December 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 8 (8) , 119-138
- https://doi.org/10.1017/s014338570000938x
Abstract
A theorem is proved giving a condition under which certain standing wave solutions of non-linear Schrödinger-type equations are linearly unstable. The eigenvalue equations for the linearized operator at the standing wave can be analysed by dynamical systems methods. A positive eigenvalue is then shown to exist by means of a shooting argument in the space of Lagrangian planes. The theorem is applied to a situation arising in optical waveguides.Keywords
This publication has 11 references indexed in Scilit:
- Instability of standing waves in nonlinear optical waveguidesPhysics Letters A, 1986
- The Sturm theorems and symplectic geometryFunctional Analysis and Its Applications, 1986
- Instability of nonlinear bound statesCommunications in Mathematical Physics, 1985
- Modulational Stability of Ground States of Nonlinear Schrödinger EquationsSIAM Journal on Mathematical Analysis, 1985
- Nonlinear Surface PolaritonsPublished by Springer Nature ,1985
- Nonlinear surface plasmons guided by thin metal filmsOptics Letters, 1984
- Orbital stability of standing waves for some nonlinear Schr dinger equationsCommunications in Mathematical Physics, 1982
- Isolated Invariant Sets and the Morse IndexCBMS Regional Conference Series in Mathematics, 1978
- Characteristic class entering in quantization conditionsFunctional Analysis and Its Applications, 1967
- On the iteration of closed geodesics and the sturm intersection theoryCommunications on Pure and Applied Mathematics, 1956