Solutions And Its Properties Of Two Shallow Water Wave Equations

This paper mainly discussed about solutions and its properties of two shallow water wave equations. And it is divided into four parts as following:In the first chapter, we firstly introduce the generation and development of soliton theory, the common methods of solving the soliton equations accurately, and the hot problems of the current research on integrable shallow water wave equations.In the second chapter,we applied the nonlinearized method based on Lax pair to give the algebro-geometric solutions of cKdV equation.In the third chapter, we considered the properties of solutions of the Cauchy problem of Novikov equation with weakly dissipative term, mainly including the local well-posedness of strong solution, the blow-up phenomenon, the lower bound of the maximal existence time, the global weak solution and the local well-posedness of periodic case.In the fourth chapter, we applied Kato’s theory to obtain the local well-posedness of two-component Novikov equation in the Sobolev space HS(R) x Hs(R),s>3/2.