Riemann-hilbert Method And The Solution Of Several Special Integrable Equations

This paper mainly discusses the application of Riemann-Hilbert method in solving nonlinear equations.It is divided into three parts:Part 1,the Riemann-Hilbert method was used to study the high order dispersion NLS(HDNLS)equation.The detail structure of the Riemann-Hilbert problem,the solving process,and the multiple soliton solutions for the equations of general expression are given.The parameters and propagation characteristics of a single soliton solution are analyzed.Then,we find the peak value and propagation direction of the single soliton solution,and get the parameters of position and shape.Finally,the expression and the figure of the solution are given.Part 2,the Riemann-Hilbert method was used to study the Chen-Lee-Liu(C-L-L)equation.Predecessors use two symmetries of the system potential matrix to construct the multisoliton solution.On the basis of them,we apply the three pairs of symmetric relations of the potential matrix of the C-L-L equation to construct two multi-soliton solutions.Then we analyze the two solutions,and prove the consistency of them.Part 3,the Riemann-Hilbert method is used to study the multi-component defocusing Hirota(MCDH)system.We get the multi-soliton solution of this system and apply RiemannHilbert method to the + 1 × + 1 matrix spectral problem.