Abstract
We study the amplitude modulation of a symmetric regularized long-wave equation with quartic nonlinearity through the use of the reductive perturbation method by introducing a new set of slow variables. The nonlinear Schrödinger (NLS) equation with seventh order nonlinearity is obtained as the evolution equation for the lowest order term in the perturbation expansion. It is also shown that the NLS equation with seventh order nonlinearity assumes an envelope type of solitary wave solution.
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Demiray, H. A note on the amplitude modulation of symmetric regularized long-wave equation with quartic nonlinearity. J Eng Math 77, 181–186 (2012). https://doi.org/10.1007/s10665-012-9538-0
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DOI: https://doi.org/10.1007/s10665-012-9538-0