CYLINDRICAL QUASI-SOLITONS OF THE ZAKHAROV-KUZNETSOV EQUATION

Evolutions and interactions of two-dimensional solitary waves of the Zakharov-Kuznetsov equation are investigated numerically. Formations of cylindrical bell-shaped pulses are observed in the initial value problems. A single bell-shaped pulse propagates stably without any deformation like a soliton. Two similar pulses exchange their amplitudes without merging and two dissimilar ones undergo overtaking collision. After a collision of two pulses, the strong pulse becomes somewhat stronger and the weak one becomes weaker with radiation of ripples, so that the collision process is slightly inelastic. Generated ripples are very small for center-to-center collision of similar pulses. The cylindrically symmetric pulses of the Zakharov-Kuznetov equation are thus found to behave approximately soliton-like. Some properties of collision process are interpreted in terms of the conservation laws. © 1990.