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Modulational instability and the Fermi‐Pasta‐Ulam recurrence

 

作者: Peter A. E. M. Janssen,  

 

期刊: Physics of Fluids(00319171)  (AIP Available online 1981)
卷期: Volume 24, issue 1  

页码: 23-26

 

ISSN:0031-9171

 

年代: 1981

 

DOI:10.1063/1.863242

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The long‐time behavior of the modulational instability of the nonlinear Schro¨dinger equation is investigated. Linear stability analysis shows that a finite amplitude uniform wave train is unstable to infinitesimal modulational perturbations with sufficiently long wavelengths while it is stable for perturbations with short wavelengths. Near the threshold for instability, the long‐time behavior of the unstable modulation is obtained by means of the multiple time scale technique. As a result, the Fermi–Pasta–Ulam recurrence is rediscovered, in agreement with recent experiments and with a numerical solution of the problem at hand.

 

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