Coalescence of Ripplons, Breathers, Dromions and Dark Solitons

Abstract

New solutions of several nonlinear evolution equations (NEEs) are obtained by a special limit corresponding to a coalescence or merger of wavenumbers. This technique will yield the multiple pole solutions of NEEs if ordinary solitons are involved. This limiting process will now be applied through the Hirota bilinear transform to other novel solutions of NEEs. For ripplons (self similar explode-decay solutions) such merger yields interacting self similar solitary waves. For breathers (pulsating waves) this coalescence gives rise to a pair of counterpropagating breathers. For dromions (exponentially decaying solutions in all spatial directions) this merger might generate additional localized structures. For dark solitons such coalescence can lead to a pair of anti-dark (localized elevation solitary waves on a continuous wave background) and dark solitons.