Numerical simulation of cylindrical solitary waves in periodic media

Numerical simulation of cylindrical solitary waves in periodic media. Quezada de Luna, M. & Ketcheson, D. I. Journal of Scientific Computing, 2013.

Paper abstract bibtex

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.

@article{ quezada2011,
  abstract = {We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.},
  annote = {In press.  Pre-print available at http://arxiv.org/abs/1209.5164.},
  archiveprefix = {arXiv},
  arxivid = {1209.5164},
  author = {{Quezada de Luna}, Manuel and Ketcheson, David I.},
  date-modified = {2013-06-23 06:22:58 +0000},
  journal = {Journal of Scientific Computing},
  keywords = {heterogeneous media, nonlinear waves, p-system, periodic media, solitary waves, soliton interaction},
  local-url = {/Users/ketch/Documents/Mendeley Desktop/Quezada de Luna, Ketcheson/2012 - Numerical simulation of cylindrical solitary waves in periodic media.pdf},
  title = {Numerical simulation of cylindrical solitary waves in periodic media},
  url = {http://arxiv.org/abs/1209.5164},
  year = {2013},
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  bdsk-url-1 = {http://arxiv.org/abs/1209.5164}
}

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Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.},\n annote = {In press. Pre-print available at http://arxiv.org/abs/1209.5164.},\n archiveprefix = {arXiv},\n arxivid = {1209.5164},\n author = {{Quezada de Luna}, Manuel and Ketcheson, David I.},\n date-modified = {2013-06-23 06:22:58 +0000},\n journal = {Journal of Scientific Computing},\n keywords = {heterogeneous media, nonlinear waves, p-system, periodic media, solitary waves, soliton interaction},\n local-url = {/Users/ketch/Documents/Mendeley Desktop/Quezada de Luna, Ketcheson/2012 - Numerical simulation of cylindrical solitary waves in periodic media.pdf},\n title = {Numerical simulation of cylindrical solitary waves in periodic media},\n url = {http://arxiv.org/abs/1209.5164},\n year = {2013},\n bdsk-file-1 = {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},\n bdsk-url-1 = {http://arxiv.org/abs/1209.5164}\n}</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" id=\"abstract_quezada2011\"\n style=\"display:none\">\n We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.\n</div>\n\n\n</div>\n","downloads":0,"keyword":["heterogeneous media","nonlinear waves","p-system","periodic media","solitary waves","soliton interaction"],"bibbaseid":"quezadadeluna-ketcheson-numericalsimulationofcylindricalsolitarywavesinperiodicmedia-2013","urls":{"Paper":"http://arxiv.org/abs/1209.5164"},"role":"author","year":"2013","url":"http://arxiv.org/abs/1209.5164","type":"article","title":"Numerical simulation of cylindrical solitary waves in periodic media","local-url":"/Users/ketch/Documents/Mendeley Desktop/Quezada de Luna, Ketcheson/2012 - Numerical simulation of cylindrical solitary waves in periodic media.pdf","keywords":"heterogeneous media, nonlinear waves, p-system, periodic media, solitary waves, soliton interaction","key":"quezada2011","journal":"Journal of Scientific Computing","id":"quezada2011","date-modified":"2013-06-23 06:22:58 +0000","bibtype":"article","bibtex":"@article{ quezada2011,\n abstract = {We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. 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