Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation
Xiao-Man Zhang1, Yan-Hong Qin1, Li-Ming Ling1*, and Li-Chen Zhao2,3,4*
1School of Mathematics, South China University of Technology, Guangzhou 510640, China 2School of Physics, Northwest University, Xi'an 710127, China 3Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China 4Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
Abstract：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.
Rogers C and Schief W K 2002 Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory (Cambridge: Cambridge University Press)
[37]
Matveev V and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
[38]
Gu C H, Hu H S, and Zhou Z X 2005 Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry (Dordrecht: Springer)
2021, Vol. 38 
