On the stability of solitary wave solutions of the fifth-order KdV equation

The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky (Physica D 3 (1981) 428) that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results. (C) 1997 Elsevier Science B.V.