Numerical Computation of the Critical Energy Constant for Two-dimensional Boussinesq Equations

摘要

The critical energy constant is of significant interest for the theoretical and numerical analysis of Boussinesq type equations. In the one-dimensional case this constant is evaluated exactly. In this paper we propose a method for numerical evaluation of this constant in the multi-dimensional cases by computing the ground state. Aspects of the numerical implementation are discussed and many numerical results are demonstrated.