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Volume 2,     Number 3,     Summer 1994

 

ON THE STABILITY OF FINITE-DEPTH
CAPILLARY-GRAVITY WAVES BY MEANS OF
THE FOURTH ORDER EVOLUTION EQUATION
MARK JONES

Abstract. A weakly nonlinear method is used to derive a fourth order evolution equation which models the three-dimensional motion of a capillary-gravity wavetrain of slowly varying amplitude in a channel of fixed finite depth. This equation is a generalization of the cubic nonlinear Schrödinger equation which has been used in previous studies of this motion. The stability of the wavetrain to long wave perturbations is examined.

 

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