Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation
(2022) In Studies in Applied Mathematics 149(1). p.95-123- Abstract
Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension-breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev–Petviashvili (KP) equation, the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line solitary waves of fKP-I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line solitary waves for both fKP-I and fKP-II equations.
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https://lup.lub.lu.se/record/857a0476-fcdb-4cb2-b029-c2fdaa3c496b
- author
- Borluk, Handan ; Bruell, Gabriele and Nilsson, Dag LU
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- dimension-breaking bifurcation, exponential time differencing, fractional Kadomtsev–Petviashvili equation, Petviashvili iteration, solitary waves, transverse instability
- in
- Studies in Applied Mathematics
- volume
- 149
- issue
- 1
- pages
- 95 - 123
- publisher
- Wiley-Blackwell
- external identifiers
-
- scopus:85126886841
- ISSN
- 0022-2526
- DOI
- 10.1111/sapm.12494
- language
- English
- LU publication?
- no
- id
- 857a0476-fcdb-4cb2-b029-c2fdaa3c496b
- date added to LUP
- 2022-04-19 15:50:26
- date last changed
- 2023-10-26 15:01:03
@article{857a0476-fcdb-4cb2-b029-c2fdaa3c496b,
abstract = {{<p>Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension-breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev–Petviashvili (KP) equation, the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line solitary waves of fKP-I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line solitary waves for both fKP-I and fKP-II equations.</p>}},
author = {{Borluk, Handan and Bruell, Gabriele and Nilsson, Dag}},
issn = {{0022-2526}},
keywords = {{dimension-breaking bifurcation; exponential time differencing; fractional Kadomtsev–Petviashvili equation; Petviashvili iteration; solitary waves; transverse instability}},
language = {{eng}},
number = {{1}},
pages = {{95--123}},
publisher = {{Wiley-Blackwell}},
series = {{Studies in Applied Mathematics}},
title = {{Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation}},
url = {{http://dx.doi.org/10.1111/sapm.12494}},
doi = {{10.1111/sapm.12494}},
volume = {{149}},
year = {{2022}},
}