From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic sol...From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.展开更多
The residual symmetry of the generalized Kaup-Kupershmidt （KKK） equation is obtained from the truncated Painleve expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solution...The residual symmetry of the generalized Kaup-Kupershmidt （KKK） equation is obtained from the truncated Painleve expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Frthermore, the gKK equation is proved to integrable in the sense of owning consistent Riecati expansion and some new Bgcklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11405110,11275129,and 11472177)the Natural Science Foundation of Zhejiang Province of China(Grant No.LY18A050001)
文摘From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11405110,11275129,11472177the Natural Science Foundation of Zhejiang Province of China under Grant Nos.LY18A050001 and LQ13A050002
文摘The residual symmetry of the generalized Kaup-Kupershmidt （KKK） equation is obtained from the truncated Painleve expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Frthermore, the gKK equation is proved to integrable in the sense of owning consistent Riecati expansion and some new Bgcklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given.
