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Evolution of higher-order gray Hirota solitary waves

Journal Article


Abstract


  • The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to detmine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary wave tail are derived. A subtle and complex picture of the development of solitary wave tails emerges. It is found that solitary wave tails develop for two reasons, one is decay of the solitary wave caused by resonance, the second is corrections at first-order to the background wave. Strong agreement is found between the theoritical predictions of the perturbation theory and numerical solutions of the governing equations.

Publication Date


  • 2008

Citation


  • Hoseini, S. & Marchant, T. R. (2008). Evolution of higher-order gray Hirota solitary waves. Studies in Applied Mathematics, 121 (2), 117-139.

Scopus Eid


  • 2-s2.0-49249088084

Number Of Pages


  • 22

Start Page


  • 117

End Page


  • 139

Volume


  • 121

Issue


  • 2

Abstract


  • The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to detmine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary wave tail are derived. A subtle and complex picture of the development of solitary wave tails emerges. It is found that solitary wave tails develop for two reasons, one is decay of the solitary wave caused by resonance, the second is corrections at first-order to the background wave. Strong agreement is found between the theoritical predictions of the perturbation theory and numerical solutions of the governing equations.

Publication Date


  • 2008

Citation


  • Hoseini, S. & Marchant, T. R. (2008). Evolution of higher-order gray Hirota solitary waves. Studies in Applied Mathematics, 121 (2), 117-139.

Scopus Eid


  • 2-s2.0-49249088084

Number Of Pages


  • 22

Start Page


  • 117

End Page


  • 139

Volume


  • 121

Issue


  • 2