Existence of periodic travelling-wave solutions of nonlinear, dispersive wave equations

DOI10.1088/0951-7715/17/6/003zbMath1086.35087OpenAlexW2066537896MaRDI QIDQ4652938

Hongqiu Chen

Publication date: 28 February 2005

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/17/6/003

zbMATH Keywords

Fourier transformBanach spacesBenjamin-Ono equationtopological-degree theoryBenjamin equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

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Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ Vector solitons of a coupled Schrödinger system with variable coefficients ⋮ Solitary waves for an internal wave model ⋮ Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems ⋮ On the existence of solitary waves for an internal system of the Benjamin-Ono type ⋮ A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models ⋮ Existence of periodic travelling wave solutions for a regularized Benjamin-Ono system ⋮ Solving nonlinear non-local problems using positive square-root operators ⋮ Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential ⋮ 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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