Abstract
This work focuses on the (2+1)-dimensional nonlinear Schrödinger equation for the propagation of ultrashort pulses in nonlinear metamaterials. With the aid of ansatz method, a various types of exact combined solitary wave solutions describing both bright and dark solitons in the same expression are presented along with the corresponding existence conditions for Kerr law and parabolic law nonlinearities. Such combined solitary waves can exhibit abundant forms including bright, anti-dark, grey (dark), W-shaped solitons or plane waves. The results presented here reveal that nonlinear metamaterials can support the co-propagation of bright and dark solitons in various combined forms.
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