For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the ...For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.展开更多
Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji et al in their auxiliary equation method. By using this method and these new solutions the com...Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji et al in their auxiliary equation method. By using this method and these new solutions the combined Korteweg-de Vries （KdV） and modified KdV （mKdV） equation and （2＋1）-dimensional Broer-Kaup-Kupershmidt system are investigated and abundant exact travelling wave solutions are obtained that include new solitary wave solutions and triangular periodic wave solutions.展开更多
In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pro...In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.展开更多
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010014)the National Natural Science Foundation of China(Grant Nos.11326164,11401528,11435005,and 11375090)
文摘For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.
基金Project supported by the National Natural Science Foundation of China （Grant No 10472029）.
文摘Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji et al in their auxiliary equation method. By using this method and these new solutions the combined Korteweg-de Vries （KdV） and modified KdV （mKdV） equation and （2＋1）-dimensional Broer-Kaup-Kupershmidt system are investigated and abundant exact travelling wave solutions are obtained that include new solitary wave solutions and triangular periodic wave solutions.
基金the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.
