Methods of investigation of solitary waves and reversible shock structures in elastic tubes

Abstract: The paper is devoted to methods of calculation and analysis of solutions of equations of elastic tube with controlled pressure and for tube filled by fluid. Membrane model and plate model are used for tube. Methods of numerical analysis are applied. Boussinesq equation is used for description of waves in the region near the instability of homogeneous states and for verification of numerical methods also. Solitary waves and shocks for this equation are investigated. Then the same methods are used for complete equations. Solitary waves and reversible shocks (generalized kinks) are investigated. Method based on calculation of eigenfunction is used for investigation of stability of solitary waves. Methods of general theory of reversible shocks are used for investigation of kinks.Note: Research direction:Mathematical problems and theory of numerical method