In　this　paper,　we　prove　the　existence　of　multi-solitons,　multi-breathers,　the　mixed　form　of　solitons　and　breathers　as　well　as　two　types　X　solitary　waves　of　the　(2+1)-dimensional　nonlinear　Schrödinger　equation　with　power　law　nonlinearity,　from　hierarchies　of　shallow　water　wave　solutions　of　the　Kadomtsev–Petviashvili　model,　inheriting　their　complex　dynamics,　which　include　fusion　and　fission　phenomena,　that　opens　a　new　path　to　obtain　multi-dimensional　optical　extreme　waveforms.　Our　numerical　results　give　a　good　approximation　for　their　simulations　and　dynamics.　©　2021　Elsevier　GmbH