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 Schrodinger equation and the Korteweg-de Vries equati...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 Schrodinger 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.展开更多
Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonline...Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonlinear Schrödinger equation(n-NLSE)are usually derived by the methods of integrable systems.In this paper,we utilize the multi-stage physics-informed neural networks(MS-PINNs)algorithm to derive the data-driven symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition.The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11771151,12022513,11775176)the Guangzhou Science and Technology Program(Grant No.201904010362)+1 种基金the Fundamental Research Funds for Central Universities(Grant No.2019MS110)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2018KJXX-094)。
文摘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 Schrodinger 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.
基金supported by National Natural Science Foundation of China(Grant Nos.11771151,61571005,and 61901160)the Science and Technology Program of Guangzhou(Grant No.201904010362)the Fundamental Research Program of Guangdong Province,China(Grant No.2020B1515310023)。
文摘Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonlinear Schrödinger equation(n-NLSE)are usually derived by the methods of integrable systems.In this paper,we utilize the multi-stage physics-informed neural networks(MS-PINNs)algorithm to derive the data-driven symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition.The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.
