论文标题
在有限域上的Hénon方程的不对称解的数值验证
Numerical verification for asymmetric solutions of the Hénon equation on bounded domains
论文作者
论文摘要
Hénon方程是Emden方程的广义形式，它可以在横向速度与径向速度的一定比例中允许对称性分叉。因此，即使在这种域上没有不对称的单向溶液，它在对称域上具有不对称溶液。我们讨论了一种数值验证方法，以证明在有限域上存在Hénon方程的解决方案。通过将方法应用于线段域和正方形结构域，我们从数值上证明了Hénon方程的解决方案的存在，以代表横向与径向速度的比率的几个参数。结果，我们找到了一组未发现的解决方案，在方形域上有三个峰。
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.
