Abstract
In this paper, we study the exact traveling wave solutions for five high-order nonlinear wave equations using the dynamical system approach. Based on Cosgrove’s work and the dynamical system method, infinitely many soliton solutions and quasi-periodic solutions are presented in an explicit form. We show the existence of uncountably infinite many double-humped solitary wave solutions. We discuss the parameters range as well as geometrical explanation of soliton solutions.
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This research was partially supported by the National Natural Science Foundation of China (11571318, 11162020).
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Li, J., Zhou, Y. Exact Solutions in Invariant Manifolds of Some Higher-Order Models Describing Nonlinear Waves. Qual. Theory Dyn. Syst. 18, 183–199 (2019). https://doi.org/10.1007/s12346-018-0283-2
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DOI: https://doi.org/10.1007/s12346-018-0283-2