Higher-order Hamiltonian Model for Unidirectional Water Waves

29 Apr 2017  ·  Bona J. L., Carvajal X., Panthee M., Scialom M. ·

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type... The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer time scale. The initial-value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by way of a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely. read more

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Analysis of PDEs