A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate eq...A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provi...The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provided by taking different "seeds".展开更多
文摘A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
基金Project supported by the National Basic Aesearch Project of Nonlinear Science (No.HH4712),and the Ministry of Education of Chi
文摘The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provided by taking different "seeds".
