New solutions and their properties in two dimensional integrable systems

It is well-known that there are two kinds of Davey-Stewartson (DS) equation, i..e, DSI and DSII, for different physical settings. In this talk,  DS is illustrated as an example of two dimensional integrable systems to explore the new localized solution. We will provide genuine two-dimensional rogue wave solution for the DSII and the lump solution for the DSI, and their properties. This talk is based on two papers joint with several co-authors: Physical Review Research 2(2020) 033376 (2020); Physical Review E  105(2022) 014218 (2022).