Zero-background rogue waves in 1D and 2D nonlinear models remain open

Determine whether rogue-wave solutions excited on zero background exist in nonlinear wave models with one spatial dimension (1+1-dimensional) and with two spatial dimensions (2+1-dimensional), and characterize these solutions if they exist.

Background

The paper motivates its paper by noting that research on rogue waves in (1+1)-dimensional nonlinear models is comparatively mature, whereas work on (2+1)-dimensional models lags behind. In particular, the authors emphasize that the topic of rogue waves excited on zero background is not well understood in either one-spatial or two-spatial settings.

They proceed to investigate this question for the (2+1)-dimensional KdV equation via a self-mapping transformation that allows construction of several types of two-dimensional rogue waves (line-soliton-induced, dromion-induced, lump-induced), aiming to contribute to this open area.

References

Particularly, the RWs excited on zero-background in both one-spatial and two-spatial nonlinear models are still basically open.

— Rogue waves excitation on zero-background in the (2+1)-dimensional KdV equation (2405.11228 - Zhang et al., 18 May 2024) in Introduction (paragraph before Eq. (1))