An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion
Holger R. DullinDepartment of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom. [email protected]Georg A. GottwaldDepartment of Mathematical Sciences, Loughborough University, Loughborough, United KingdomDarryl D. HolmDepartment of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom
2001en
ABI
Abstract
We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.
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