Author
Borluk, Handan, Bruell, G., Nilsson, D.
Publication Date
2024-01
Publication Place
-
Springer
Subject
Decay of lump solutions, Existence of lump solutions, Fractional Kadomtsev-Petviashvili equation (primary), Petviashvili iteration
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1311-0454
Record ID
69b66d9e-a8af-4855-8d61-7796bdcd06bd
Library Location
Natural and Mathematical Sciences
Date
2024-01
Notes
Wallenberg foundation
Sample Text
Of 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.
DOI
10.1007/s13540-023-00236-2
Cilt
27
