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Solitons and modulation theory

2009

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Soliton Perturbation Theory For A Higher-Order Hirota Equation, Tim Marchant Dec 2008

Soliton Perturbation Theory For A Higher-Order Hirota Equation, Tim Marchant

Tim Marchant

Solitary wave evolution for a higher order Hirota equation is examined. For the higher order Hirota equation resonance between the solitary waves and linear radiation causes radiation loss. Soliton perturbation theory is used to determine the details of the evolving wave and its tail. An analytical expression for the solitary wave tail is derived and compared to numerical solutions. An excellent comparison between numerical and theoretical solutions is obtained for both right- and left-moving waves. Also, a two-parameter family of higher order asymptotic embedded solitons is identified.