The general theory of discontinuities in nondissipative dispersive models had been developed. Discontinuity in this theory is any stationary transition between uniform, periodic, quasiperiodic or stohastic states. The theory includes the method of prediction of the type of discontinuity, observation of this discontinuity in numerical experiment, evolution condition analysis, methods to determine boundary conditions for the discontinuity, derivation and solution of averaged equations for wave zones, methods to obtain the shock structure as a solution of ordinary equation systems. One method is based on representation of shock structure as the special soliton-like solution, methods to obtain solitary or generalized solitary wave solution had been developed also.
Main publications:
Bakholdin I. B., Il'ichev A. T. Radiation and modulational instability described by the fifth-order Korteweg–de Vries equation // Contemporary Mathematics, 1996, v. 200, p. 1–15.
