Abstract
Oceanic water waves are actively investigated. One example is a variable-coefficient nonlinear dispersive-wave system modelling the long gravity water waves in a shallow oceanic environment. The system describes the surface velocity of the water wave and the wave elevation. Making use of symbolic computation, we perform the Painlevé analysis and work out two sets of the bilinear forms, two sets of the N-soliton solutions and one set of the similarity reductions for the aforementioned system, with N being a positive integer. We also graphically discuss those soliton solutions. What we accomplish should rely on the variable coefficients. This paper could be of some use for the future oceanic studies.
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