Nonlinear stability problems for the sine-Gordon equation
- 1 February 1973
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (2) , 267-276
- https://doi.org/10.1063/1.1666308
Abstract
Two stability problems for the nonlinear sine‐Gordon equation are studied. The stability of a class of time independent (static) solutions is studied using linear dynamic stability theory. An asymptotic approximation of the nonlinear transient response to small disturbances of an unstable static state is obtained by the two time method. Interpretations of the results are given for the continuous pendulum problem and for the Josephson tunnel junction. A proof of the validity of the asymptotic approximation is given.Keywords
This publication has 6 references indexed in Scilit:
- Transient Behavior of Unstable Nonlinear Systems with Applications to the Bénard and Taylor ProblemsSIAM Journal on Applied Mathematics, 1971
- Nonlinear dynamic buckling of a compressed elastic columnQuarterly of Applied Mathematics, 1971
- A simple nonlinear dynamic stability problemBulletin of the American Mathematical Society, 1970
- A Nonlinear Klein-Gordon EquationAmerican Journal of Physics, 1969
- Periodic vibrations of systems governed by nonlinear partial differential equationsCommunications on Pure and Applied Mathematics, 1966
- Josephson-type superconducting tunnel junctions as generators of microwave and submillimeter wave radiationProceedings of the IEEE, 1966