论文标题
Cubic Whitham方程的呼气解决方案
Breather Solutions to the Cubic Whitham Equation
论文作者
论文摘要
我们关注的是Cubic Whitham方程的呼吸溶液的数值近似值，该方程是界面波的水波模型。该模型将强大的非线性与水波问题的非本地特征结合在一起。如孤立波的非弹性相互作用所暗示的，该方程是不可积分的。作为一个非本地模型，它以低频限制为众所周知的修改KDV（MKDV）方程，它是一个完全可整合的模型。 MKDV方程具有呼吸溶液，即时间周期性，并将其定位在空间两次溶液中。最近表明，这些呼吸溶液自然而然地表现为不变积分的基态，这表明至少在近似意义上，这种结构也可能存在于不可融合模型中。在这项工作中，我们提供了数值证据，即在不可综合的情况下，也可能存在呼吸溶液。
We are concerned with numerical approximations of breather solutions for the cubic Whitham equation which arises as a water-wave model for interfacial waves. The model combines strong nonlinearity with the non-local character of the water-wave problem. The equation is non-integrable as suggested by the inelastic interaction of solitary waves. As a non local model, it generalizes, in the low frequency limit, the well known modified KdV (mKdV) equation which is a completely-integrable model. The mKdV equation has breather solutions, i.e. periodic in time and localized in space biparametric solutions. It was recently shown that these breather solutions appear naturally as ground states of invariant integrals, suggesting that such structures may also exist in non-integrable models, at least in an approximate sense. In this work, we present numerical evidence that in the non-integrable case of the cubic Whitham equation, breather solutions may also exist.
