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Lump solutions of the fractional Kadomtsev–Petviashvili equation

Borluk, Handan ; Bruell, Gabriele and Nilsson, Dag LU (2024) In Fractional Calculus and Applied Analysis 27(1). p.22-63
Abstract

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... (More)

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.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Decay of lump solutions, Existence of lump solutions, Fractional Kadomtsev-Petviashvili equation (primary), Petviashvili iteration
in
Fractional Calculus and Applied Analysis
volume
27
issue
1
pages
42 pages
publisher
De Gruyter
external identifiers
  • scopus:85181907786
ISSN
1311-0454
DOI
10.1007/s13540-023-00236-2
language
English
LU publication?
yes
id
62c7afaf-d3bb-4f65-9392-9be35a7807f9
date added to LUP
2024-02-12 10:34:32
date last changed
2024-02-12 10:37:07
@article{62c7afaf-d3bb-4f65-9392-9be35a7807f9,
  abstract     = {{<p>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&gt;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&gt;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.</p>}},
  author       = {{Borluk, Handan and Bruell, Gabriele and Nilsson, Dag}},
  issn         = {{1311-0454}},
  keywords     = {{Decay of lump solutions; Existence of lump solutions; Fractional Kadomtsev-Petviashvili equation (primary); Petviashvili iteration}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{22--63}},
  publisher    = {{De Gruyter}},
  series       = {{Fractional Calculus and Applied Analysis}},
  title        = {{Lump solutions of the fractional Kadomtsev–Petviashvili equation}},
  url          = {{http://dx.doi.org/10.1007/s13540-023-00236-2}},
  doi          = {{10.1007/s13540-023-00236-2}},
  volume       = {{27}},
  year         = {{2024}},
}