On the Geometry of Bäcklund Transformations

Geometry of Bäcklund Transformations II: Monge-Ampère Invariants

This article is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank-$1$ Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler-Lagrange systems of distinct types.

几何对一类马氏体相变标度律的影响

On the Effect of Geometry on Scaling Laws for a Class of Martensitic Phase Transformations

本文研究二维马氏体相变奇异摄动问题的标度律，证明几何不相容导致对数损失，并揭示一般区域与高相容多边形区域之间的线性—对数二分法。