Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations

DOI10.1016/J.AML.2019.02.003zbMath1412.35198arXiv1905.08380OpenAlexW2913816749MaRDI QIDQ1739448

Alexei Rybkin

Publication date: 26 April 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.08380

zbMATH Keywords

shallow water wave equationsCarrier-Greenspan transform

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (3)

Run-up of long waves on background shear currents ⋮ Inverse problem for the nonlinear long wave runup on a plane sloping beach ⋮ Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves

Cites Work

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• Rogue waves in nonlinear hyperbolic systems (shallow-water framework)
• Water waves of finite amplitude on a sloping beach
• Hodograph Transformations of Linearizable Partial Differential Equations
• Solving the nonlinear shallow-water equations in physical space
• The runup of solitary waves
• A Modern Introduction to the Mathematical Theory of Water Waves
• Tsunami run-up and draw-down on a plane beach
• Nonlinear evolution and runup–rundown of long waves over a sloping beach
• Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier–Greenspan approach
• Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations

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