Journal
PHYSICAL REVIEW LETTERS
Volume 87, Issue 19, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.87.194501
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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-Holtn (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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