Low-regularity Solutions Of A Class Of Nonlinear Dispersive Wave Equations

Nonlinearity is universal and important phenomenon in nature. Most nonlinear problems can be described by nonlinear equations. In recent years, many nonlinear partial differential equations were derived from physics, mechanics, chemistry, biology, engineering, aeronautics, medicine, economy, finance and many other fields. Because of the non-linearity and complexity of themselves, it is a great challenge to deal with them. In this paper, we study a class of nonlinear partial differential dispersive equations, that is, general Degasperis-Procesi equation, the Fornberg-Whitham equation.In this paper, Low-regularity solutions of the periodic Fornberg-Whitham equation and general Degasperis-Procesi equation are studied by using the relationship between weak solutions and distribution solutions on the Lipschitz space and so on. Then the periodic peakons are given by considering the traveling wave solution, and we prove that they satisfy the condition of distribution solutions. Therefore we get the constructions.There are four sections in this paper.In the first section, we introduce the background and actuality and summarize the main result.In the second section, we will introduce the basic theory, basic concepts needed in the study's.In the third section, we introduce the main results about low-regularity solutions of the periodic Fornberg-Whitham equation, prove them and verify their correctness. In the forth section, we introduce the main results about low-regularity solutions of the periodic general Degasperis-Procesi equation, prove them and verify their correctness.