Painlev′e Integrablity And Solutions Of (2+1)-dimensional High-order Broer-Kaup System

Soliton theory as one of the hot research nonlinear science, which has a wide range ofapplications in theoretical physics, nonlinear optics, and life sciences research fields . In solitontheory , integrability of nonlinear equations is always of vital importance for almost all of theresearch problems. So the integrable properties of nonlinear di?erencial equations are importantin nonlinear science. Futhermore, with the continuous development of science and technology,more and more new methods seeking exact solutions emission continuously, making the nonlinearequations have more in-depth study. In the thesis, two higher order Broer-Kaup equations arestudied:In the first chapter, we introduce the history and development of soliton and researchprofiles, at the same time introduce the main work of this thesis.In the second chapter, we discuss the (2+1)-dimentional BK equations's Painlev′e inte-grability by means of the standard WTC approach and apply the standard truncation, thenon-standard truncation, the F-function expansion method with a computerized symbolic com-putation for solving the N-soliton solutions, one-soliton solutions and solitary wave solutions.In the third chapter, using the standard WTC approach, exponential function, tanh func-tion method , we obtain a series of exact solutions of the variable coe?cient BK equations.In the forth chapter, we summarize our main results.