Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation Supported by the National Natural Science Foundation of China (Grant Nos. 11771151, 12022513, and 11775176), the Guangzhou Science and Technology Program (Grant No. 201904010362), the Fundamental Research Funds for Central Universities (Grant No. 2019MS110), and the Major Basic Research Program of Natural Science of Shaanxi Province (Grant No. 2018KJXX-094)

For a scalar integrable model, it is generally believed that the solitons interact with each other elastically, for instance, multi-bright solitons from the nonlinear Schrödinger equation and the Korteweg-de Vries equation, etc. We obtain double-valley dark solitons from the defocusing Hirota equation by the Darboux transformation. Particularly, we report a remarkable phenomenon for the inelastic interaction of the double-valley dark solitons, in contrast to the solitons interacting with each other elastically for a scalar integrable model in previous works. Furthermore, we give the explicit conditions for the elastic collision based on the asymptotic analysis results. It is shown that the double-valley dark solitons could also admit elastic interaction under the special parameters settings. [ABSTRACT FROM AUTHOR]