Lump solutions of the fractional Kadomtsev–Petviashvili equation
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Type :
Article
Publication Status :
Published
Access :
openAccess
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
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 existence of lump solutions and their decay. Moreover, numerically, we observe cross-sectional symmetry of lump solutions for the fKP-I equation.
Source :
Fractional Calculus and Applied Analysis
Date :
2024-01
Volume :
27
Issue :
1
Publisher :
Springer
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