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
|Publication status||Published - 2020 Feb 6|
- Elliptic boundary value problem
- Henon equation
- Numerical verification
- Symmetry-breaking bifurcation
ASJC Scopus subject areas