Capillary Solitary Waves and Their Disintegration on the Shelf

Vladan D. Djordjević

The interest in studying various problems of nonlinear wave theory in the presence of some kind of inhomogeneity in the direction of the wave propagation has increased very much recently. The source of inhomogeneity in the case of surface waves is mostly the varying depth of liquid, in the case od magneto-acoustic waves in а plasma - the varying density of plasma, in the case of lattice waves - the varying mass etc. lt has been shown in аll these cases that the problem reduces to one of well known equations of nonlinear wave theory, as for example Korteweg-de Vries (K-dV) equation, nonlinear SchrOdinger (NL-S) equation and others, with varying coefficients. K-dV equation with varying coefficients for surface waves was derived Ьу Kakutani (1971а), for magneto-acoustic waves bу Kakutani (1971b) and Ьу Asano and Ono (1971) and for lattice waves bу Ono (1972). А general form of NL-S equation with varying coefficients was conjectured bу Ono (1974) and the concrete equation for surface waves was derived Ьу Djordjević and Redekopp (1977а).