Lump solutions of the fractional Kadomtsev–Petviashvili equation
(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
- Borluk, Handan ; Bruell, Gabriele and Nilsson, Dag LU
- organization
- publishing date
- 2024-02
- 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>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.</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}}, }