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Hopf-Cole transformation via generalized Schrödinger bridge problem

Published 25 Jan 2019 in math.DS, math.AP, and math.OC | (1901.09051v1)

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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Authors (2)

  1. Flavien Léger 
  2. Wuchen Li 

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