Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Abstract

Coupled nonlinear Schrödinger equations, linked by cross modulation terms, arise in both nonlinear optics and in Rossby waves in the atmosphere and ocean. Numerically, Akhmediev and Ankiewicz and Haelterman and Sheppard discovered a class of soiltary waves which are composed of a tall, narrow sech-shaped soliton in one mode, bound to a pair of short, wide sech-shaped peaks in the other mode or polarization. Through the method of matched asymptotic expansions, we derive analytical approximations to these solitary waves, and to their periodic generalization, which have been hitherto accessible only through numerical computation.