MULTI-SPEED SOLITARY WAVES IN SPIN-1 BOSE-EINSTEIN CONDENSATES

This paper investigates the existence of multi-speed solitary waves in spin-1 BoseEinstein condensates, governed by the three-component Gross-Pitaevskii equations. These multi-speed solitary waves manifest as vector solitary waves, with each component propagating at a different speed. By utilizing scaling invariance, Galilean drift, and solving the system backward in time using energy methods, we establish the existence of multi-speed solitary wave solutions. The presence of these waves implies that solitary wave excitations in one component can propagate independently without significantly affecting the other components. Furthermore, we analyze the asymptotic behavior of the magnetic soliton, which is driven by the particle exchange and corresponds to the net magnetization of the system.