Abstract:
The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg–de Vries equation.
Key words:shallow water theory of a fluid, cubic nonlinearities in the wave equations, dispersion relation, approximate perturbation technique.
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