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Note on slightly unstable nonlinear wave systems

Published online by Cambridge University Press:  29 March 2006

Richard Habermant
Richard Habermant
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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Abstract

The asymptotic solution for large time of the initial-value problem for weakly nonlinear wave systems is obtained by the method of matched asymptotic expansions in the case in which the linearized problem is slightly unstable. The linearized solution is valid until its small exponential growth overcomes the algebraic decay due to the dispersion of the initial energy. For larger times the nonlineax terms become important, but there are no additional dispersive or diffusive effects. For the non-diffusive case an exact solution which enables the explicit verification of the asymptotic results is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 1 , 20 March 1973 , pp. 129 - 142
Copyright
© 1973 Cambridge University Press

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References

Benney, D. J. & Newell, A. C. 1967 J. Math. & Phys. 46, 133–139.
Hocking, L. M. & Stewartson, K. 1972 Proc. Roy. Soc. A 326, 289–313.
Hocking, L. M., Stewartson, K. & Stuart, J. T. 1972 J. Fluid Mech. 51, 705–735.
Landau, L. D. 1944 Dokl. Akad. Naulc. Sssr, 44, 311–314.
Newell, A. C., Lance, C. G. & Aucoin, P. A. 1970 J. Pluid Mech. 40, 513–542.
Newell, A. C. & Whitehead, J. A. 1971 Proc. Iutam Symp. Instab. Cont. Syst. Herrenalb 1969, pp. 284–289.
Stewartson, K. & Stuart, J. T. 1971 J. Fluid Mech. 48, 529–545.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353–370.
Stuart, J. T. 1971 Ann. Rev. Fluid Mech. 3, 347–370.