The existence of the solitary wave and the nonexistence of kink (anti-kink) wave solutions are studied for a perturbed (1 + 1)-dimensional dispersive long wave equation. The methods are based on the geometric singular perturbation (GSP, for short) approach, Melnikov method and bifurcation analysis. The results show that the solitary wave solution with a suitable wave speed c and parameter κ exists under the small singular perturbation. Interestingly, unlike solitary wave solutions, the kink (anti-kink) wave solution doesn't persist because the corresponding Melnikov function has no zeros. Further, numerical simulations are utilized to verify the correctness of our analytical results.
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