Highlights ? Kinds of vector soliton are presented on nonzero background. ? Interplay between different kinds of nonlinear waves can be observed analytically. ? Hard-wall like reflection between them are possible to emerge. Abstract Soliton solutions are presented on nontrivial backgrounds of the coupled system which governs the evolution of electromagnetic wave propagating in nonlinear left-handed materials. We find that there are much more abundant structural solitons or Akhmediev breathers than the ones on trivial background. The hard-wall like reflection effects are observed during the collision of bright, dark, Akhmediev breather with Akhmediev breathers. There are possibilities to observe that one dark soliton (Akhmediev breather) collides with an Akhmediev breather and emerges into another dark soliton (Akhmediev breather) in the coupled system.
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