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- Title
Solitons and rogue waves for a nonlinear system in the geophysical fluid.
- Authors
Xie, Xi-Yang; Tian, Bo; Liu, Lei; Wu, Xiao-Yu; Jiang, Yan
- Abstract
In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with , which reflects the collision between the wave packet and mean flow, , which measures the state of the basic flow, and group velocity . is observed to affect the amplitudes of the solitons, and can influence the solitons' traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. has no effects on A, which is the amplitude of the wave packet, but with the increase of , amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When is chosen differently, A and B do not keep their shapes invariant. With the value of increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with increasing, amplitude of B decreases, but has no effects on A. Collision features of A and B alter with the value of changing. When we make the value of larger, amplitudes of A and B increase.
- Subjects
SOLITONS; ROGUE waves; GEOPHYSICAL fluid dynamics; NONLINEAR systems; DARBOUX transformations; WAVE packets; COLLISIONS (Physics)
- Publication
Modern Physics Letters B, 2016, Vol 30, Issue 35, p-1
- ISSN
0217-9849
- Publication type
Article
- DOI
10.1142/S0217984916504121