Periodic traveling-wave solutions of nonlinear dispersive evolution equations

DOI10.3934/DCDS.2013.33.4841zbMath1277.35096OpenAlexW2319412367MaRDI QIDQ379620

Hongqiu Chen, Jerry L. Bona

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2013.33.4841

zbMATH Keywords

stability theorygeneralized cnoidal waveslarge wavelength limitnonlocal dispersion relations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Series solutions to PDEs (35C10) Soliton equations (35Q51) Initial value problems for PDEs with pseudodifferential operators (35S10) Traveling wave solutions (35C07) Soliton solutions (35C08) PDEs in connection with geophysics (35Q86)

Related Items (8)

Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems ⋮ Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities ⋮ Periodic travelling waves for a fourth order nonlinear evolution equation ⋮ Global well-posedness for \(H^{-1}(\mathbb{R})\) perturbations of KdV with exotic spatial asymptotics ⋮ An example of non-decreasing solution for the KdV equation posed on a bounded interval ⋮ Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler function ⋮ Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation

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