Papers › Highest Cusped Waves for the Fractional KdV Equations
Highest Cusped Waves for the Fractional KdV Equations
Joel Dahne
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In this paper we prove the existence of highest, cusped, traveling wave solutions for the fractional KdV equations fₜ + f fₓ = |D|^α fₓ for all α∈(-1,0) and give their exact leading asymptotic behavior at zero. The proof combines careful asymptotic analysis and a computer-assisted approach.
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