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Periodic traveling--wave solutions of nonlinear dispersive evolution equations

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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.
    Mathematics Subject Classification: Primary: 35C07, 35C08, 35Q35, 35Q51, 35Q53, 35S10, 76B15, 76B25; Secondary: 35C10, 35Q86, 86A05.


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