KdV breathers on a cnoidal wave background

Using the Darboux transformation for Korteweg-de Vries equation, we construct and analyze exact solutions describing interaction of a solitary wave traveling cnoidal wave. Due to their unsteady, wavepacket-like character, these patterns are referred as breathers. Both elevation (bright) depression (dark) breather obtained. The nonlinear dispersion relations demonstrate that bright breathers propagate faster (slower) than background Two-soliton obtained in limit degeneration In small amplitude regime, dark accurately approximated by soliton Schr\"odinger equation. These results provide insight into recent experiments on soliton-dispersive shock interactions gases.