By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-Kd...By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-KdV equation, the Sine-Gordon equation and the Sinh-Gordon equation are derived.展开更多
Nonlocal symmetries related to the B?cklund transformation(BT)for the modified KdV-sine-Gordon(mKdV-SG)equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transfor...Nonlocal symmetries related to the B?cklund transformation(BT)for the modified KdV-sine-Gordon(mKdV-SG)equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations.Then through the parameter expansion procedure,an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived.Finally,several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.展开更多
基金Supported by the National Science Foundation of Education Department of Henan Province（2011B110013）
Acknowledgement The authors would like to express their sincere thanks to Professor Wang Mingliang for his enthusiastic help and encouragement.
文摘By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-KdV equation, the Sine-Gordon equation and the Sinh-Gordon equation are derived.
基金financial support by the National Natural Science Foundation of China(Grant Nos.11675055 and 12071302)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘Nonlocal symmetries related to the B?cklund transformation(BT)for the modified KdV-sine-Gordon(mKdV-SG)equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations.Then through the parameter expansion procedure,an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived.Finally,several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.
