Modulational instability of cnoidal wave solutions of the modified Korteweg–de Vries equation
- 1 July 1976
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (7) , 1196-1200
- https://doi.org/10.1063/1.523044
Abstract
The stability of cnoidal wavetrain solutions of the modified Korteweg–de Vries equation is analyzed using Whitham’s modulational theory. The cnoidal waves are solutions of an oscillator equation obtained by twice integrating the modified Korteweg–de Vries equation. The stability of the cnoidal waves is determined by the roots of the polynomial in the oscillator equation. For real roots the waves are stable, whereas for complex roots the waves are unstable.Keywords
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