Abstract
The celebrated Gardner model is a hybrid nonlinear equation resulting from merging the well-known KdV and mKdV and a perturbed dissipative term. In Zhou et al. (Pramana-J Phys 88:69, 2017), the geometric perturbation theory is used to prove the existence of soliton solutions to this model when the embedded perturbation parameter is sufficiently small. In this work, we aim to extract different type solutions to this model by means of the celebrated unified method. Also, we revisited the Klein–Gordon system that supports the study of long-wave dynamics of discrete models (Alagesan et al. in Chaos Solitons Fractals 21:879–882, 2004) and extracted more new solutions. Finally, all the obtained solutions are verified and categorized for both models.
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