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 th
e 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 gi
ves rise to a pair of counterpropagating breathers. For dromions (exponenti
ally decaying solutions in all spatial directions) this merger might genera
te additional localized structures. For dark solitons such coalescence can
lead to a pair of anti-dark (localized elevation solitary waves on a contin
uous wave background) and dark solitons.