Asymptotic collision properties of multiple antidark and dark soliton pairs in partially and fully space-shifted 𝒫𝒯 -symmetric nonlocal Davey–Stewartson I equations

This paper explores the asymptotic collision properties of multiple pairs of antidark and dark solitons in the partially space-shifted (P-SS) and fully space-shifted (F-SS) 𝒫𝒯 -symmetric nonlocal Davey–Stewartson I (NDSI) equations. In the P-SS 𝒫𝒯 -symmetric NDSI equation, the two solitons of each single soliton pair intersect head-on in ( x , y ) plane, whereas they exhibit parallel intersections in the F-SS 𝒫𝒯 -symmetric NDSI equation. To investigate the asymptotic collision properties of multiple soliton pairs, we conduct asymptotic analysis as y→±∞ for the soliton pair solutions of the P-SS 𝒫𝒯 -symmetric NDSI equation, and as t→±∞ for the soliton pair solutions of the F-SS 𝒫𝒯 -symmetric NDSI equation. Based on the asymptotic analysis, the states of N soliton pairs in these two NDSI equations are categorized. The N soliton pairs possess a total of 2N+1 different non-degenerate states and N(2N+1) distinct degenerate states in the P-SS 𝒫𝒯 -symmetric NDSI equation, while they have 2N+1 different non-degenerate states and (3N+1)N/2 distinct degenerate states in the F-SS 𝒫𝒯 -symmetric NDSI equation. A highly unique state of the N soliton pairs is identified only in the P-SS 𝒫𝒯 -symmetric NDSI equation, wherein all the 2 N solitons vanish into the background. Our asymptotic results also indicate that the SS factor x_0 in the P-SS 𝒫𝒯 -symmetric DSI equation, as well as the SS factor pair (x_0, y_0) in the F-SS 𝒫𝒯 -symmetric DSI equation, selectively influence individual solitons within their respective soliton pairs, while leaving the other soliton in each pair unaffected.