Numerical verification for asymmetric solutions of the Henon equation on the unit square

Taisei Asai; Kazuaki Tanaka; Shin'ichi Oishi

Numerical verification for asymmetric solutions of the Henon equation on the unit square

Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi

Research output: Contribution to journal › Article › peer-review

Abstract

The Henon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We numerically prove the existence of asymmetric solutions of the Henon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of solutions with three peaks. The bifurcation curves of such solutions are shown for a square domain.

MSC Codes 85A15, 35J25

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 Feb 6

Keywords

Elliptic boundary value problem
Henon equation
Numerical verification
Symmetry-breaking bifurcation

ASJC Scopus subject areas

General

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title = "Numerical verification for asymmetric solutions of the Henon equation on the unit square",

abstract = "The Henon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We numerically prove the existence of asymmetric solutions of the Henon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of solutions with three peaks. The bifurcation curves of such solutions are shown for a square domain.MSC Codes 85A15, 35J25",

keywords = "Elliptic boundary value problem, Henon equation, Numerical verification, Symmetry-breaking bifurcation",

author = "Taisei Asai and Kazuaki Tanaka and Shin'ichi Oishi",

year = "2020",

month = feb,

day = "6",

language = "English",

journal = "Nuclear Physics A",

issn = "0375-9474",

publisher = "Elsevier",

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T1 - Numerical verification for asymmetric solutions of the Henon equation on the unit square

AU - Asai, Taisei

AU - Tanaka, Kazuaki

AU - Oishi, Shin'ichi

PY - 2020/2/6

Y1 - 2020/2/6

N2 - The Henon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We numerically prove the existence of asymmetric solutions of the Henon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of solutions with three peaks. The bifurcation curves of such solutions are shown for a square domain.MSC Codes 85A15, 35J25

AB - The Henon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We numerically prove the existence of asymmetric solutions of the Henon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of solutions with three peaks. The bifurcation curves of such solutions are shown for a square domain.MSC Codes 85A15, 35J25

KW - Elliptic boundary value problem

KW - Henon equation

KW - Numerical verification

KW - Symmetry-breaking bifurcation

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JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

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