Research Of The Stability Waves, Global Existence And Blow-up Of Shallow Water Waves Solutions

In this paper, the major contents conclude: by using the basic concept, well posed theorem and so on , we research the orbital stability waves , global existence and blow-up phenomena of the nonlinear equations' solutions.In the third chapter, One mainly researches the stability waves of two rod equation with conserved quantities. Firstly, one gives the basically definition of the orbital stability. By transforming the rod equations into corresponding Hamilton system, one obtains four equivalent cases and validates these cases one by one. The difficulty is the fourth case. To satisfy this problem, one chooses propriety Liouville transformations so that some properties come into existence. The orbital stability of solitary waves of nonlinear equations is proved.In the forth chapter, by conserved quantities of D-P equation, we proved that the propagation speed for a shallow water equation speed is infinite. On the other hand ,we prove the global existence of solutions in D-P equation with strong dispersive term .By using well-posed theorems and deriving a conservation law, we obtain a priori estimate for the L~∞-norm of the strong solutions .This enables us to establish several global existence theorems.In the fifth chapter, we research the blow-up phenomenon of solutions in D-P equation with strong dispersive term .