Perturbation series for the double cnoidal wave of the Korteweg–de Vries equation

DOI10.1063/1.526110zbMath0558.35066OpenAlexW2070890304MaRDI QIDQ3223275

John P. Boyd

Publication date: 1984

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526110

zbMATH Keywords

Riemann theta functionsolitary wavesKorteweg-de Vries equationnumerical comparisonsalgebraic equationdouble cnoidal wavecollison phase shiftsnonlinear phase speeds

Mathematics Subject Classification ID

Solitary waves for incompressible inviscid fluids (76B25) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Miracles, misconceptions and scotomas in the theory of solitary waves, Construction of Lighthill's unitary functions: The imbricate series of unity, The double cnoidal wave of the Korteweg–de Vries equation: An overview, The special modular transformation for polycnoidal waves of the Korteweg–de Vries equation, Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform \(\mu\)-representation, Soliton Creation and Destruction, Resonant Interactions, and Inelastic Collisions in Shallow Water Waves, Double cnoidal waves of the Korteweg-de Vries equation: A boundary value approach

Cites Work

• A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
• Slowly varying solitary waves. I. Korteweg-de Vries equation
• The double cnoidal wave of the Korteweg–de Vries equation: An overview
• The special modular transformation for polycnoidal waves of the Korteweg–de Vries equation
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg–de Vries equation