Double cnoidal waves of the Korteweg-de Vries equation: A boundary value approach

DOI10.1016/0167-2789(91)90084-MzbMath0734.35119MaRDI QIDQ810761

John P. Boyd, Sue Ellen Haupt

Publication date: 1991

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

nonlinear boundary value problemKorteweg-de Vries equationDouble cnoidal wavesdouble solitonfinite amplitude solutionGalerkin algorithm

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Boundary value problems for higher-order elliptic equations (35J40) Solitary waves for incompressible inviscid fluids (76B25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Construction of Lighthill's unitary functions: The imbricate series of unity, Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation, A HAM-based analytic approach for physical models with an infinite number of singularities

Cites Work

• Solitons from sine waves: Analytical and numerical methods for non- integrable solitary and cnoidal waves
• Modeling nonlinear resonance: A modification to the Stokes' perturbation expansion
• The double cnoidal wave of the Korteweg–de Vries equation: An overview
• Perturbation series for the double cnoidal wave of the Korteweg–de Vries equation
• The special modular transformation for polycnoidal waves of the Korteweg–de Vries equation
• PLTMGC: A Multigrid Continuation Program for Parameterized Nonlinear Elliptic Systems
• An Analytical Model of Periodic Waves in Shallow Water
• Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg–de Vries equation
• Periodic solutions of the KdV equation
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• The iterative solution of non-linear ordinary differential equations in Chebyshev series
• Integrals of nonlinear equations of evolution and solitary waves
• Model equations for long waves in nonlinear dispersive systems
• Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item