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arXiv · 1901.09051

Hopf-Cole transformation via generalized Schr\"odinger bridge problem

Flavien Léger·Wuchen Li
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Abstract

We study generalized Hopf-Cole transformations motivated by the Schr\"odinger bridge problem, which can be seen as a boundary value Hamiltonian system on the Wasserstein space. We prove that generalized Hopf-Cole transformations are symplectic submersions in the Wasserstein symplectic geometry. Many examples, including a Hopf-Cole transformation for the shallow water equations, are given. Based on this transformation, energy splitting inequalities are provided.

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Flavien Léger, Wuchen Li. 2019-01-25. Hopf-Cole transformation via generalized Schr\"odinger bridge problem. https://arxiv.org/abs/1901.09051

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