Open Access. Powered by Scholars. Published by Universities.®
Higher-order Hirota equation; Asymptotic transformation; Solitary wave interaction; Higher-order coordinate and phase shifts; Embedded solitons; Soliton perturbation theory; Solitary wave tails
Articles 1 - 1 of 1
Full-Text Articles in Physics
Solitary Wave Interaction And Evolution For A Higher-Order Hirota Equation, Tim Marchant
Solitary Wave Interaction And Evolution For A Higher-Order Hirota Equation, Tim Marchant
Tim Marchant
Solitary wave interaction and evolution for a higher-order Hirota equation is examined. The higher-order Hirota equation is asymptotically transformed to a higher-order member of the NLS hierarchy of integrable equations, if the higher-order coefficients satisfy a certain algebraic relationship. The transformation is used to derive higher-order one- and two-soliton solutions. It is shown that the interaction is asymptotically elastic and the higher-order corrections to the coordinate and phase shifts are derived. For the higher-order Hirota equation resonance occurs between the solitary waves and linear radiation, so soliton perturbation theory is used to determine the details of the evolving wave and …