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.

arXiv comment29 pages, 8 figures

References in corpus (8)

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Cited by in corpus (3)

• Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
• Evolution of internal cnoidal waves with local defects in a two-layer fluid with rotation
• Robustness of mKdV Breathers: A Numerical Perspective