New localized excitations in (2+1)-dimensional integrable systems

The new localized excitations of some (2+1)-dimensional integrable models obtained by the multi-linear variable separation approach (MLVSA) are reviewed. A universal formula with some arbitrary functions is obtained for some suitable physical quantities for various integrable models. By selecting the arbitrary functions appropriately, one may obtain abundant interesting localized excitations like the multi-dromions, lumps, ring solitons, breathers, instantons, peakons, compactons, foldons, chaotic and fractal patterns and so on. The localized excitations possess quite rich interaction behaviors.