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Volume 8,     Number 3,     Fall 2000

 

INTERPRETATION OF THE STABILITY AND INSTABILITY OF THE SOLITARY WAVES GOVERNED BY A FORCED KORTEWEG-DE VRIES EQUATION
SAMUEL S. SHEN, T. BRYANT MOODIE AND BIN SHEN

Abstract. In view of the maximum height of a solitary shallow-water wave in a channel, this paper provides an interpretation of the stability and instability of the solitary waves governed by a forced Korteweg-de Vries equation. The interpretation implies Malomed's conjecture [3]: of the two cusped solitary waves of a locally forced Korteweg-de Vries equation, the lower one is stable. Numerical simulations show that the higher solitary wave degenerates into the lower, stable solitary wave and radiates a soliton upstream and a wake down stream. This is a KdV soliton but is not a stable water-surface profile because its amplitude is higher than the unstable solitary wave.

 

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© 2005, Canadian Applied Mathematics Quarterly (CAMQ)