Numerical verification for asymmetric solutions of the Hénon equation on bounded domains

Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi

Research output: Contribution to journalArticlepeer-review

Abstract

The Hénon 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 discuss a numerical verification method for proving the existence of solutions of the Hénon equation on a bounded domain. By applying the method to a line-segment domain and a square domain, we numerically prove the existence of solutions of the Hénon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of undiscovered solutions with three peaks on the square domain.

Original languageEnglish
Article number113708
JournalJournal of Computational and Applied Mathematics
Volume399
DOIs
Publication statusPublished - 2022 Jan 1

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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