KdVH has additional solitary and periodic traveling waves beyond KdV solitons, and the paper's ImEx-SBP schemes provably preserve energy and are asymptotic preserving toward KdV.
Ketcheson, Hendrik Ranocha, and Jochen Sch¨ utz
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Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation
KdVH has additional solitary and periodic traveling waves beyond KdV solitons, and the paper's ImEx-SBP schemes provably preserve energy and are asymptotic preserving toward KdV.