Darboux transformation and exact solutions of the generalized KdV equation
LI Ying
LI De-sheng
Abstract：The rapid development of the soliton theory has evoked a heated discussion among many scholars who are interested in it .The most important issue in the theory of soliton is the solutions to partial differential e -quations .This paper mainly discusses the issue of exact solutions , which solved by the Darboux transformation . Darboux transformation is an effective method for solving nonlinear partial differential equations , the method that find the relationship between the solutions to equation through finding a gauge transformation to keep the corre -sponding Lax pair invariant .The author of this paper ,firstly, from the point of spectrum in the AKNS system of generalized KdV equation ,through a series of classified discussions , having got three kinds of Darboux transfor-mations of the equation and then proved them .Then we selected the suitable trivial solutions to the equation , the new exact solutions are obtained .The generalized KdV equation has practical and theoretical role in fluid me-chanics , plasma physics and aerodynamics , so the study of the generalized KdV equation is of great significance .
Keywords：Darboux transformationgeneralized KdV equationspectral problemexact solution
Publication Date：2014-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：6( 12-16,33 )