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Title: Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation
Authors: Grimshaw, Roger H.J.
Pelinovsky, Efim N.
Talipova, Tatiana G.
Ruderman, Michael
Erdelyi, Robert
Issue Date: 2004
Abstract: The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breathers. The properties of breathers are studied both within the modified Korteweg -de Vries equation, and also within the nonlinear Schrödinger equation derived by an asymptotic reduction from the modified Korteweg -de Vries for weakly nonlinear wave packets, The associated spectral problems (AKNS or Zakharov-Shabat) of the inverse-scattering transform technique also utilized. Wave formation due to this modulational instability is investigated for localized and for periodic disturbances. Nonlinear-dispersive focusing is identified as a possible mechanism for the formation of anomalously large pulses.
Description: This pre-print has been submitted, and accepted, to the journal of Studies in Applied Mathematics. The definitve version: GRIMSHAW, R., PELINOVSKY, E., TALIPOVA, T., RUDERMAN, M. and ERDELYI, R., 2005. Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation. Studies in Applied Mathematics, 114(2),pp.189-210 is available at www.blackwell-synergy.com.
URI: https://dspace.lboro.ac.uk/2134/241
Appears in Collections:Pre-prints (Maths)

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