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Related Experiment Video

Updated: Mar 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Variational principle in optics II: Dissipative wave equations.

Jacob Rubinstein, Gershon Wolansky

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |August 10, 2016
    PubMed
    Summary

    Phase retrieval for dissipative wave equations is challenging. This study offers two solutions, one using weighted least action and another using elliptic partial differential equations for broader applicability.

    Area of Science:

    • Wave physics
    • Mathematical physics
    • Inverse problems

    Background:

    • Phase retrieval from intensity measurements is crucial in various scientific fields.
    • Dissipative wave equations present unique challenges compared to conservative systems.
    • The solvability of phase retrieval for dissipative systems remains an open question.

    Purpose of the Study:

    • To investigate the solvability of phase retrieval for dissipative wave equations.
    • To develop novel methods for solving the phase retrieval problem in dissipative systems.
    • To provide a comprehensive theoretical framework for phase retrieval in the presence of dissipation.

    Main Methods:

    • Transformation of the problem to the weighted least action principle for specific potentials.

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  • Application of advanced results from the theory of elliptic partial differential equations.
  • Solving Monge-Ampere type differential equations for general dissipative potentials.

    • Main Results:

    • A full solution is demonstrated for a class of dissipating potentials via weighted least action.
    • The problem is shown to be always solvable up to a scaling factor for all other potentials.
    • A method involving Monge-Ampere type equations is presented for the general case.

    Conclusions:

    • The phase retrieval problem for dissipative wave equations is solvable under specific conditions.
    • Novel mathematical techniques provide robust solutions for both specific and general dissipative potentials.
    • The findings advance the understanding and application of phase retrieval in complex wave phenomena.