Numerical verification for asymmetric solutions of the Hénon equation on the unit square
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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 numerically prove the existence of asymmetric solutions of the Hénon 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.
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