The long‐wave limit for the water wave problem I. The case of zero surface tension

By Guido Schneider, C. E. Wayne. 2000

223 citations recorded by the source corpus.

Subfields: Mathematical Physics, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bbd91c0302f7551f6c2a603332e13d12ef9401dd

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In Mathematical Physics

In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves (2003, background): “See Prasad and Akylas (1997); Marchant (2002); Schneider and Wayne (2000) for discussions of this point.”
Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory (2002, methodology): “Indeed, in the work of Craig [36], Kano and Nishida [42], and the more recent discussion of Schneider and Wayne [54], theoretical justification has been provided for some aspects of the passage from the Euler equations to some of the one-and two-way models considered here.”
Almost global wellposedness of the 2-D full water wave problem (2009, background): “Schneider, G., Wayne, E.: The long wave limit for the water wave problem I.”
Large time existence for 3D water-waves and asymptotics (2007, unknown): “[13,28,43,5,47,23]) and its justification is now complete.”
The zero surface tension limit two‐dimensional water waves (2005, background): “The work of Craig was extended in [15], in which a longer interval of existence was found and the dynamics of the solution over that time interval was discussed.”
Nonhomogeneous Boundary-Value Problems for One-Dimensional Nonlinear Schr\"odinger Equations (2015, methodology): “on of a more complete model. Justifying the simpler model as an approximation of a more elaborate model typically requires smoothness of the solutions of both the full and the approximate models (see [5, 34, 66] for justiﬁcation of the KdV equation as an approximation of the full water-wave problem,”
Long Wave Approximations for Water Waves (2005, methodology): “This theorem could certainly be obtained using the estimates of the Dirichlet to Neumann operators in the works of Craig [14] and Schneider & Wayne [23].”
Propagation of ultra-short optical pulses in cubic nonlinear media (2004, background): “(This fact has been proven rigorously in some related contexts such as the propagation of long-waves on a fluid surface [ 17 ].) For this reason we will concentrate on a right-moving wave packet and ignore the left-moving part of the solution in what follows.”