Borluk, HandanBruell, G.Nilsson, D.2024-02-232024-02-232024-011311-0454http://hdl.handle.net/10679/9206https://doi.org/10.1007/s13540-023-00236-2Of concern is the fractional Kadomtsev–Petviashvili (fKP) equation and its lump solution. As in the classical Kadomtsev–Petviashvili equation, the fKP equation comes in two versions: fKP-I (strong surface tension case) and fKP-II (weak surface tension case). We prove the existence of nontrivial lump solutions for the fKP-I equation in the energy subcritical case α>45 by means of variational methods. It is already known that there exist neither nontrivial lump solutions belonging to the energy space for the fKP-II equation [9] nor for the fKP-I when α≤45 [26]. Furthermore, we show that for any α>45 lump solutions for the fKP-I equation are smooth and decay quadratically at infinity. Numerical experiments are performed for the existence of lump solutions and their decay. Moreover, numerically, we observe cross-sectional symmetry of lump solutions for the fKP-I equation.engopenAccessAttribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/article271226300113961030000110.1007/s13540-023-00236-2Decay of lump solutionsExistence of lump solutionsFractional Kadomtsev-Petviashvili equation (primary)Petviashvili iteration2-s2.0-85181907786