Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation

We consider the half-wave maps (HWM) equation which is a continuum limit of classical version Haldane–Shastry spin chain. In particular, we explore many-body dynamical system arising from HWM under pole ansatz. The shown to be completely integrable by demonstrating that it exhibits Lax pair and relevant conservation lows. Subsequently, analytical multisoliton solutions are constructed means expansion method. properties one- two-soliton then investigated in detail as well their dynamics. Last, an asymptotic analysis N-soliton solution reveals no phase shifts appear after collision solitons. This intriguing feature worth noting since first example observed head-on rational A number problems remain open for equation, some discussed concluding remarks.