JournalsaihpcVol. 36, No. 2pp. 347–363

Nonlinear responses from the interaction of two progressing waves at an interface

  • Maarten de Hoop

    Computational and Applied Mathematics and Earth Science, Rice University, United States of America
  • Gunther Uhlmann

    Department of Mathematics, University of Washington, Institute for Advanced Study, the Hong Kong University of Science and Technology
  • Yiran Wang

    Department of Mathematics, University of Washington, United States of America
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Abstract

For scalar semilinear wave equations, we analyze the interaction of two (distorted) plane waves at an interface between media of different nonlinear properties. We show that new waves are generated from the nonlinear interactions, which might be responsible for the observed nonlinear effects in applications. Also, we show that the incident waves and the nonlinear responses determine the location of the interface and some information of the nonlinear properties of the media. In particular, for the case of a jump discontinuity at the interface, we can determine the magnitude of the jump.

Cite this article

Maarten de Hoop, Gunther Uhlmann, Yiran Wang, Nonlinear responses from the interaction of two progressing waves at an interface. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 347–363

DOI 10.1016/J.ANIHPC.2018.04.005