This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weie...This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.展开更多
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
基金supported by the Open Project of Key Laboratory of Mathematics Mechanization,CAS under Grant No.KLMM0602
文摘This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.
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.
