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Complexity analysis of local behaviors of a new nonlinear differential dynamic system
  • Yongli Sun,
  • Wen-Xiu Ma,
  • Jianping Yu
Yongli Sun
Beijing University of Chemical Technology
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Wen-Xiu Ma
University of South Florida
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Jianping Yu
University of Science and Technology Beijing
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Abstract

In this paper, we propose and study a (3+1)-dimensional generalized Hirota-Satsu-Ito equation, which is an important physical model. Here, by using the Hirota bilinear method, we derive its lump-type solutions, which are almost rationally localized in all spatial directions. The interaction solutions play an important roel in studying nonlinear phnoemnon, such as nonlinear optics. Thus, three kind of localized interaction solutions are constructed, respectively. In order to study the dynamic behaviours, numerical simulations are implemented, which show that there are two interesting physical phenomen: one is that fission and fusion ohenoenon happen during the collision; the other is that rogue wave phenomena is triggered by the interaction between a lump-type wave and a soliton wave (see Figure 2). The proposed (3+1)-dimensional model and results obtained can be applyied to the research on other nonlinear localized waves.