标题： 随机哈密顿卡马斯-霍姆方程的比较数值研究 显示英文标题

标题： A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations

摘要： 我们引入了一种随机扰动的Camassa-Holm方程，与之前的表述不同，能量由随机流保持。 我们将这与一种互补方法进行比较，该方法保持泊松括号的Casimirs。 通过该模型的能量保持数值实现，我们研究了噪声对解的众所周知的“peakon”形成行为的影响。 能量保持的随机方法生成了一组围绕确定性Camassa-Holm解的解，而保持Casimirs的替代方法产生的peakon可能会更显著地远离确定性解传播。 显示英文摘要

摘要： We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a complementary approach which preserves Casimirs of the Poisson bracket. Through an energy preserving numerical implementation of the model, we study the influence of noise on the well-known 'peakon' formation behaviour of the solution. The energy conserving stochastic approach generates an ensemble of solutions which are spread around the deterministic Camassa-Holm solution, whereas the Casimir conserving alternative develops peakons which may propagate away from the deterministic solution more dramatically.