Abstract
Abstract
In this paper, the rogue wave solutions of the (2+1)-dimensional Myrzakulov–Lakshmanan (ML)-IV equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation (DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained. The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.
Funder
the National Natural Science Foundation of China
the Inner Mongolia Normal University Graduate Students’ Research and Innovation Fund
the Natural Science Foundation of Inner Mongolia Autonomous Region, China
the Fundamental Research Funds for the Inner Mongolia Normal University, China
Graduate students’ research and Innovation fund of Inner Mongolia Autonomous Region
the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education
Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region
Reference38 articles.
1. Waves that appear from nowhere and disappear without a trace;Akhmediev;J. Phys. Lett. A,2009
2. The disintegration of wave trains on deep water;Benjamin;J. Fluid Mech.,1967
3. The chemical basis of morphogenesis Phil;Turing;Philos. Trans. Roy. Soc. London Ser.,1952
4. Collapse of Langmuir Waves Sov. Phys.;Zakharov;Zh. Eksp. Teor. Fiz,1972
5. Rogue periodic waves of the focusing nonlinear Schrödinger equation;Chen;Proc. R. Soc.,2018