Shallow Water Models and Their Analytical Properties

Cheviakov, Alexei; Zhao, Peng

doi:10.1007/978-3-031-53074-6_3

CMS/CAIMS Books in Mathematics

2024

DOI: 10.1007/978-3-031-53074-6_3

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Shallow Water Models and Their Analytical Properties

Alexei Cheviakov,

Peng Zhao

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2024

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Collisions of Burgers Bores with Nonlinear Waves

Dombret,

Holm,

et al. 2024

Mathematics of Planet Earth

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This chapter treats nonlinear wave-current interactions in their simplest form—as an overtaking collision. In one spatial dimension, the chapter investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations—Korteweg–de Vries (KdV) and nonlinear Schrödinger (NLS). The bore-wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT).

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Collisions of Burgers Bores with Nonlinear Waves

Dombret,

Holm,

et al. 2024

Mathematics of Planet Earth

View full text Add to dashboard Cite

show abstract

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Shallow Water Models and Their Analytical Properties

Cited by 1 publication

References 406 publications

Collisions of Burgers Bores with Nonlinear Waves

Collisions of Burgers Bores with Nonlinear Waves

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