Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

•We present unified rational solutions for describing Peregrine solitons and algebraic analogs.•The significance of the space–time correction effect is revealed.•Persistence of Peregrine solitons in defocusing Kerr media is shown.•Two interesting sorts of two-soliton states are analyzed along with distinct defining regimes.

Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.