Periodic Traveling-Wave Solutions of Nonlinear Dispersive Evolution Equations
Bona, Jerry L.
PublisherAmerican Institute of Mathematical Sciences
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For a general class of nonlinear, dispersive wave equations, existence of periodic, traveling-wave solutions is studied. These traveling waveforms are the analog of the classical cnoidal-wave solutions of the Korteweg-de Vries equation. They are determined to be stable to perturbation of the same period. Their large wavelength limit is shown to be solitary waves.
Subjectgeneralized cnoidal waves
generalized Korteweg-de Vries equations