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Title: KdV breathers on a cnoidal wave background
Abstract Using the Darboux transformation for the Korteweg–de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character, these wave patterns are referred to as breathers. Both elevation (bright) and depression (dark) breather solutions are obtained. The nonlinear dispersion relations demonstrate that the bright (dark) breathers propagate faster (slower) than the background cnoidal wave. Two-soliton solutions are obtained in the limit of degeneration of the cnoidal wave. In the small amplitude regime, the dark breathers are accurately approximated by dark soliton solutions of the nonlinear Schrödinger equation. These results provide insight into recent experiments on soliton-dispersive shock wave interactions and soliton gases.  more » « less
Award ID(s):
1816934
NSF-PAR ID:
10433854
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Physics A: Mathematical and Theoretical
Volume:
56
Issue:
18
ISSN:
1751-8113
Page Range / eLocation ID:
185701
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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