Lump solutions of the fractional Kadomtsev–Petviashvili equation

Name: Lump solutions of the fractional Kadomtsev–Petviashvili equation
Author: Borluk, Handan, Bruell, G., Nilsson, D.

İsim	Lump solutions of the fractional Kadomtsev–Petviashvili equation
Yazar	Borluk, Handan, Bruell, G., Nilsson, D.
Basım Tarihi:	2024-01
Basım Yeri	- Springer
Konu	Decay of lump solutions, Existence of lump solutions, Fractional Kadomtsev-Petviashvili equation (primary), Petviashvili iteration
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1311-0454
Kayıt Numarası	69b66d9e-a8af-4855-8d61-7796bdcd06bd
Lokasyon	Natural and Mathematical Sciences
Tarih	2024-01
Notlar	Wallenberg foundation
Örnek Metin	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

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Lump solutions of the fractional Kadomtsev–Petviashvili equation

Yazar Borluk, Handan, Bruell, G., Nilsson, D.

Basım Tarihi 2024-01

Basım Yeri - Springer

Konu Decay of lump solutions, Existence of lump solutions, Fractional Kadomtsev-Petviashvili equation (primary), Petviashvili iteration

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1311-0454

Kayıt Numarası 69b66d9e-a8af-4855-8d61-7796bdcd06bd

Lokasyon Natural and Mathematical Sciences

Tarih 2024-01

Notlar Wallenberg foundation

Örnek Metin 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