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- Title
Bilinear auto-Bäcklund transformations, breather and mixed lump–kink solutions for a (3+1)-dimensional integrable fourth-order nonlinear equation in a fluid.
- Authors
Meng, Fan-Rong; Tian, Bo; Zhou, Tian-Yu
- Abstract
In this paper, we investigate a (3+1)-dimensional integrable fourth-order nonlinear equation that can model both the right- and left-going waves in a fluid. Based on the Hirota method, we derive three sets of the bilinear auto-Bäcklund transformations along with some analytic solutions. Through the extended homoclinic test approach, we obtain some breather solutions. We find that the breather propagates steadily along a straight line, with one hole and one peak in each period. Graphical investigation indicates that the coefficients in that equation affect the location and shape of the breather. Moreover, we construct some mixed lump–kink solutions. Fusion and fission between a lump wave and a kink soliton are analyzed graphically. The solutions addressed in this paper may be applied to mimic some complex waves in fluids.
- Subjects
NONLINEAR equations; WAVES (Fluid mechanics); SINE-Gordon equation; COMPLEX fluids; FLUIDS; BACKLUND transformations
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2024, Vol 38, Issue 18, p1
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S0217979224502321