The total integral of the Boussinesq–type equations for surface gravity long waves in the form Kulikovsky–Drozdova form is found. The equations of Kulikovsky–Drozdova published in 1996 describes waves in channel. Nonstationary flow of a viscoplastic medium between two parallel plates was considered for the case of varying pressure gradient. The problem is reduced to the Stephan problem. Four multiparameter family of exact solutions are found. The new modification of a method of an average of a Hamilton systems is offered. The method is based on analytical expression of the Poincare maps in parametrical form. The developed method gives an asymptotic solution of a problem about a spherical pendulum with arbitrary vibration of a suspension point. The motion of particles of an incompressible viscous and visco-plastic mediums in thin layer whose boundary varies in a periodic way was investigated. Transition to the globally dynamical chaos is described.
Main publications:
Klimov D. M., Petrov A. G. Analytical solutions of the boundary-value problem of nonstationary flow of viscoplasic medium between two plates // Archive of Applied Mechanics. V. 70. 2000. p. 3–16.
