Complexity analysis of local behaviors of a new nonlinear differential
dynamic system
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.