Model equations for long waves in nonlinear dispersive systems

@article{Benjamin1972ModelEF,
  title={Model equations for long waves in nonlinear dispersive systems},
  author={Thomas Brooke Benjamin and Jerry L. Bona and J. J. Mahony},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  year={1972},
  volume={272},
  pages={47 - 78}
}
  • T. Benjamin, J. Bona, J. Mahony
  • Published 30 March 1972
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Several topics are studied concerning mathematical models for the unidirectional propagation of long waves in systems that manifest nonlinear and dispersive effects of a particular but common kind. Most of the new material presented relates to the initial-value problem for the equation ut+ux+uux−uxxt=0,(a), whose solution u(x,t) is considered in a class of real nonperiodic functions defined for ࢤ∞ <x< ∞,t≥0. As an approximation derived for moderately long waves of small but finite amplitude in… 
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  • J. Bona, P. J. Bryant
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1973
An initial-boundary-value problem for the equation is considered for x, t ≥ 0. This system is a model for long water waves of small but finite amplitude, generated in a uniform open channel by a
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In this paper, we obtain new nonlinear systems describing the interaction of long water waves in both two and three dimensions. These systems are symmetric and conservative. Rigorous convergence
The stability of solitary waves
  • T. Benjamin
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
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The Korteweg-de Vries equation, which describes the unidirectional propagation of long waves in a wide class of nonlinear dispersive systems, is well known to have solutions representing solitary
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  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1972
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