Inverse Scattering Transforming For TD Equation

The regularization of the Riemann-Hilbert problem is applied to study the TD equa-tion and the soliton solutions of the TD equation are obtained. By virtue of the inverse scattering transform method, the analytic properties of the spectral problem associated with the TD equation are discussed, and then a nonregular martrix Riemann-Hilbert prob-lem with zero is constructed, and the relationship between the solution of TD equation and that of the Riemann-Hilbert problem is established.The nonregular Riemann-Hilbert problem discussed in this article involves the simple zeros. The author constructs a repre-sentation of the solution of TD equation about the soliton matrix, and finally obtains the one soliton solutions.