Abstract
In this work, we explore a variety of solitary wave ansatze and periodic wave ansatze to some nonlinear equations. Three complex systems of nonlinear equations that appear in mathematical physics are investigated. We derive abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota–Maccari system. The results obtained show that these three coupled equations exhibit the richness of explicit solutions: solitons, periodic and rational wave solutions.
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