Nonlinear interaction of waves in elastodynamics and an inverse problem

  • Maarten de Hoop
  • Gunther UhlmannEmail author
  • Yiran Wang


We consider nonlinear elastic wave equations generalizing Gol’dberg’s five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements of the nonlinear responses, we solve the inverse problem of determining elastic parameters from the displacement-to-traction map.



Maarten V. de Hoop acknowledges and sincerely thanks the Simons Foundation under the MATH\(+\)X program for financial support. He was also partially supported by the members of the Geo-Mathematical Imaging Group at Rice University and NSF under grant DMS-1815143. Gunther Uhlmann is partially supported by NSF and a Si-Yuan Professorship at HKUST.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Maarten de Hoop
    • 1
  • Gunther Uhlmann
    • 2
    • 3
    Email author
  • Yiran Wang
    • 4
  1. 1.Computational and Applied Mathematics and Earth ScienceRice UniversityHoustonUSA
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA
  3. 3.Institute for Advanced StudyThe Hong Kong University of Science and TechnologyClear Water BayHong Kong
  4. 4.Department of MathematicsStanford UniversityStanfordUSA

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