In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described...In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.展开更多
In this paper,we study normal families of meromorphic functions.By using the idea in[16],we obtain some normality criteria for families of meromorphic functions concerning the wandering multiple functions,which extend...In this paper,we study normal families of meromorphic functions.By using the idea in[16],we obtain some normality criteria for families of meromorphic functions concerning the wandering multiple functions,which extend and improve the well-known Montel's criterion,Bloch-Valiron's theorem,and the related results due to Carathéodory,and Grahl-Nevo et al..展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12361052)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414)+3 种基金the Fundamental Research Funds for the Inner Mongolia Normal University,China(Grant Nos.2022JBTD007,2022JBXC013)Graduate Students'Research and Innovation Fund of Inner Mongolia Autonomous Region(Grant No.B20231053Z)the Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application(Inner Mongolia Normal University),the Ministry of Education(Grant Nos.2023KFZR01,2023KFZR02)the First-Class Disciplines Project,Inner Mongolia Autonomous Region,China(Grant No.YLXKZX-NSD-001)。
文摘In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.
基金supported by Jiangsu Natural Science fund for Colleges and Universities(06KJD110175)Natural Science Fund of Xuzhou Institute of Technology(XKY2008310)
文摘In this paper,we study normal families of meromorphic functions.By using the idea in[16],we obtain some normality criteria for families of meromorphic functions concerning the wandering multiple functions,which extend and improve the well-known Montel's criterion,Bloch-Valiron's theorem,and the related results due to Carathéodory,and Grahl-Nevo et al..
