论文标题
Hirota-Satsuma动力学作为KDV方程的非偏见限制
Hirota-Satsuma Dynamics as a Non-Relativistic Limit of KdV Equations
论文作者
论文摘要
我们考虑一个由两个耦合的KDV方程组成的系统（一个用于左移动者，另一个用于右手），并在BMS $ _3 $ _3 $/gca $ _2 $ sommetry的意义上研究了其超偏见和非相关限制。我们表明，无论原始相对论的哈密顿量中的耦合常数如何，系统都没有具有正能量的系统的局部超忠实限制。相比之下，只要左和右移动之间存在非零的耦合，就存在具有正能量的局部非相关性极限。在这些限制中，波动方程将（IV型）降低为hirota-satsuma动力学并变得可集成。因此，在这种情况下，高能物理学的输入有助于非线性科学 - 在这种情况下，发现了KDV和Hirota-Satsuma的综合结构之间的限制关系。
We consider a system of two coupled KdV equations (one for left-movers, the other for right-movers) and investigate its ultra-relativistic and non-relativistic limits in the sense of BMS$_3$/GCA$_2$ symmetry. We show that there is no local ultra-relativistic limit of the system with positive energy, regardless of the coupling constants in the original relativistic Hamiltonian. By contrast, local non-relativistic limits with positive energy exist, provided there is a non-zero coupling between left- and right-movers. In these limits, the wave equations reduce to Hirota-Satsuma dynamics (of type IV) and become integrable. This is thus a situation where input from high-energy physics contributes to nonlinear science - in this case, uncovering the limiting relation between integrable structures of KdV and Hirota-Satsuma.
