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Nonlinear interaction of positive and negative energy modes in Hamiltonian systems

Content Provider	Scilit
Author	Denier, J. P. Grimshaw, R. H. J.
Copyright Year	1990
Description	We consider the nonlinear evolution of a Hamiltonian system as the system passes through a linear resonance (as the system parameters vary). Two cases are considered. In the first case the linearized problem (at resonance) possess a full complement of normal mode solutions. This case is presented in the context of the interaction between modes which may have oppositely signed energy. The second case considered has an additional degeneracy in that the linearized problem (at resonance) has a single normal mode solution. Both cases are analysed using normal form theory and in both cases the systems governing the transition through resonance are shown to be completely integrable in the classical sense. Possible bifurcations as the resonance is traversed are discussed. Conditions for the existence of algebraic singularities at some finite positive time are also presented.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/897C918B71C92C5564AC4E9CC8213D57/S0334270000006755a.pdf/div-class-title-nonlinear-interaction-of-positive-and-negative-energy-modes-in-hamiltonian-systems-div.pdf
Ending Page	424
Page Count	28
Starting Page	397
ISSN	03342700
e-ISSN	18394078
DOI	10.1017/s0334270000006755
Journal	The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
Issue Number	4
Volume Number	31
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1990-04-01
Access Restriction	Open
Subject Keyword	The Journal of the Australian Mathematical Society. Series B. Applied Mathematics Linearized Problem Normal Mode
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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