The special modular transformation for polycnoidal waves of the Korteweg–de Vries equation

DOI10.1063/1.526111zbMath0558.35067OpenAlexW1987229592MaRDI QIDQ3223276

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/10.1063/1.526111

zbMATH Keywords

Riemann theta functionsolitary wavesKorteweg-de Vries equationnumerical comparisonsimplicit dispersion relationmodular transformationcollision phase shiftsdouble cnoidal waveparameter regimesnonlinear phase speedsN-polycnoidal waves

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

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, Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform \(\mu\)-representation, A HAM-based analytic approach for physical models with an infinite number of singularities, 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
• Perturbation series for the double cnoidal wave of the Korteweg–de Vries equation
• Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg–de Vries equation