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The Cauchy problem of a shallow water equation. (English) Zbl 1095.35041
The authors consider the initial value problem for a fifth order shallow water equation in the nonperiodic case, as opposed to the previously considered periodic case. The equation studied has the same nonlinear terms as the well-known Fuchssteiner-Fokas-Camassa-Holm equation, and in this sense can be considered to be a higher order analogue of this last.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:
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[7] Bourgain, J.: Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I, Schrödinger equations. GAFA, 3, 107--156 (1993) · Zbl 0787.35097 · doi:10.1007/BF01896020
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