TY - JOUR

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

AU - Asai, Taisei

AU - Tanaka, Kazuaki

AU - Oishi, Shin'ichi

N1 - Publisher Copyright:
Copyright © 2020, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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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M3 - Article

AN - SCOPUS:85093149809

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -