The structure of twodimensional solitons in media with anomalously small dispersion
Abstract
It is shown that in some cases the dispersion coefficient in the frequency expansion for twodimensional solitons may approach zero in the longwave limit (e.g., in the case of gravitational capillary waves in shallow water or skewed magnetoacoustic waves in cold plasma). Stationary solutions to the KadomtsevPetviashvili equation for twodimensional multisolitons are derived to limit the dispersion term. The solutions have damping oscillatory asymptotics in the direction of soliton motion, and monotonically decreasing asymptotics in the transverse direction. It is shown that soliton amplitudes should exceed a certain threshold value which is determined by the parameters of the equation. Estimates of the characteristic amplitudes and velocities of water wave solitons are presented.
 Publication:

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
 Pub Date:
 May 1985
 Bibcode:
 1985ZhETF..88.1616A
 Keywords:

 Nonlinear Evolution Equations;
 Solitary Waves;
 Water Waves;
 Wave Dispersion;
 Wave Equations;
 Amplitudes;
 Asymptotic Properties;
 Damping;
 Propagation Velocity;
 Taylor Series;
 Physics (General)