Abstract
Hybrid rogue wave and breather solutions of the nonlinear coupled dispersionless evolution equations are studied by Darboux transformation. Firstly, a new Darboux transformation is constructed for the coupled dispersionless evolution equations. The solutions of the appropriate Lax pair are selected to construct the hybrid solutions. Nth-order breather solutions are derived by N-step Darboux transformation. Besides, different parameters have different effects on the hybrid solutions. These results are of great significance for understanding the relevant physical phenomena in nonlinear optics.
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