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This analysis extends estimates for solutions of linear Korteweg–de Vries equations, implying new insights into fractional dispersion.
As an example in their complex variables textbook, Mark Ablowitz and Athanassios Fokas apply the method of steepest descent to derive an asymptotic estimate for the solution of the linear Korteweg–de Vries (KdV) equation for large times. Here the analysis is extended to an equation with a fractional dispersion relation that contains this KdV equation (which models dispersion), the heat equation (diffusion), and the one-way wave equation (advection) as special cases.
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Weideman et al. (2026) studied this question.
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