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Abstract

The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky [Physica D, 3 (1981) 428-438] that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results
Original languageEnglish
PublisherUniversity of Bristol
Number of pages6
DOIs
Publication statusPublished - Oct 1996

Bibliographical note

Additional information: Later published by Elsevier Science, (1997) Physics Letters A, 233 (1-2), pp. 58-62. ISSN 0375-9601

Keywords

  • asymptotic theory
  • Korteweg-de Vries equation
  • multi-pulsed stationary solitary wave solutions
  • gravity-capillary water waves
  • fifth-order-derivative dispersive perturbation
  • Gorshkov and Ostrovsky
  • two-pulses

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