Journal
NONLINEAR DYNAMICS
Volume 97, Issue 4, Pages 2413-2423Publisher
SPRINGER
DOI: 10.1007/s11071-019-05137-9
Keywords
Benjamin-Bona-Mahony equation; Solitary wave; Geometric singular perturbation theory; Melnikov integral
Categories
Funding
- Natural Science Foundations of China [11771082]
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In this manuscript, based on the geometric singular perturbation theory, several new solitary wave solutions in a perturbed generalized Benjamin-Bona-Mahony (BBM) equation are detected by the explicit calculation of the associated Melnikov integrals. These solitary wave solutions are homoclinic to non-trivial steady states and have not been found before. We also determine the zeroth-order approximations to the speeds of these solitary waves explicitly. In the calculations of the Melnikov integrals, the explicit expressions of the unperturbed homoclinic orbits play an important role.
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