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A perturbation method for non-linear dispersive waves with an application to water waves

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Summary

A multiple scale perturbation method is developed to obtain asymptotic evolution equations for slowly varying wave train solutions to non-linear dispersive wave problems. The method appears to give results which are a generalization of Whitham's theory on one hand and a generalization of the ray theory on the other hand. First an application is given to a non-linear Klein-Gordon equation, then the method is applied to two-dimensional water waves on water of finite depth (Stokes waves).

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Authors and Affiliations

  1. Department of Mathematics, University of Groningen, Groningen, The Netherlands

    H. W. Hoogstraten & R. Van Der Heide

Authors
  1. H. W. Hoogstraten
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  2. R. Van Der Heide
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Hoogstraten, H.W., Van Der Heide, R. A perturbation method for non-linear dispersive waves with an application to water waves. J Eng Math 6, 341–353 (1972). https://doi.org/10.1007/BF01535195

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  • DOI: https://doi.org/10.1007/BF01535195

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