Darboux Transformation Of A Third-Order Soliton Equation And Its Exact Solutions

In this thesis,the Darboux transformation and explicit solutions of a nonlinear evo-lution equation associated with a 3 × 3 matric spectral problem are studied.Firstly,the equation associated with the spectral problem can be derived according to the known Lax pairs.Secondly,the Darboux Transformation can be obtained based on the gauge trans-formation.Finally,by choosing suitable seed solutions a group of explicit solutions can be derived from the linear algebraic system.