Explicit solutions of the reduced Ostrovsky equation

E.J. Parkes

doi:10.1016/j.chaos.2005.10.028

Explicit solutions of the reduced Ostrovsky equation

E.J. Parkes

Mathematics And Statistics

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54 Citations (Scopus)

Abstract

It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].

Original language	English
Pages (from-to)	602-610
Number of pages	8
Journal	Chaos, Solitons and Fractals
Volume	31
Issue number	3
DOIs	https://doi.org/10.1016/j.chaos.2005.10.028
Publication status	Published - Feb 2007

Keywords

fractals
chaos theory
vakhnenko equation
physics

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10.1016/j.chaos.2005.10.028

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title = "Explicit solutions of the reduced Ostrovsky equation",

abstract = "It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].",

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N2 - It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].

AB - It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].

KW - fractals

KW - chaos theory

KW - vakhnenko equation

KW - physics

UR - http://dx.doi.org/10.1016/j.chaos.2005.10.028

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DO - 10.1016/j.chaos.2005.10.028

M3 - Article

SN - 0960-0779

VL - 31

SP - 602

EP - 610

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 3

ER -

Explicit solutions of the reduced Ostrovsky equation

Abstract

Keywords

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