2023/04/20 by Handan Borluk, Gabriele Bruell, Borluk, Handan +3
Mathematics · Medicine · Physics and Astronomy · #35Q35 #35S30 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2304.10257
openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Of concern are lump solutions for the fractional Kadomtsev--Petviashvili (fKP) equation. 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>(4)/(5) 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 nor for the fKP-I when α≤ (4)/(5). Furthermore, we show that for any α>(4)/(5) 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.