The Generalized Dressing Method For A Class Of Soliton Equations

This thesis is focused on solving the modified nonlinear Schrodinger equation (MNLS equation)by generalized dressing method where u= 0 is taken as the trivial seed solution of MNLS equation.First of all, starting from two matrix equations of compatibility condition to the system, the Jost solution is introduced by virtue of the spectral problem related to the Lax pair of MNLS equation. It is found that the Jost solution to this first order differential equation is not independent, but satisfies the symmetry condition. Consequently, the analyticity of Jost function is analyzed and various matrix forms of the initial differential operator are discussed. The structure of the matrix is determined and the matrix satisfies both the symmetry condition and the relation of Jost function. After that, the definition matrix RH problem is mainly discussed. In order to determine the potential function, it is necessary to construct the linear equations of discrete eigenfunction. We choose the canonical solution of RH problem. The selection of dressing factor is very important to solve soliton equation by dressing method. At the last part, the soliton solution of the original equation is obtained according to the selected dressing factor. Figures of soliton solution are illustrated simultaneously.