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

Research output: Contribution to journalArticlepeer-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 languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Feb 6

Keywords

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

ASJC Scopus subject areas

  • General

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