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A model for the two-way propagation of water waves in a channel. (English) Zbl 0332.76007

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35L60 First-order nonlinear hyperbolic equations
35F25 Initial value problems for nonlinear first-order PDEs
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References:
[1] Boussinesq, Comptes Rendus de l’Academie des Sciences 73 pp 256– (1871)
[2] DOI: 10.1098/rsta.1975.0035 · Zbl 0306.35027 · doi:10.1098/rsta.1975.0035
[3] DOI: 10.1098/rsta.1972.0032 · Zbl 0229.35013 · doi:10.1098/rsta.1972.0032
[4] Benjamin, Lectures in Applied Mathematics 15 (1974)
[5] Yosida, Functional analysis (1971) · doi:10.1007/978-3-662-00781-5
[6] DOI: 10.1017/S0022112071002295 · Zbl 0229.76011 · doi:10.1017/S0022112071002295
[7] Peregrine, Journal of Hydraulic Research 12 pp 141– (1974) · doi:10.1080/00221687409499762
[8] DOI: 10.1017/S0022112069002461 · doi:10.1017/S0022112069002461
[9] DOI: 10.1017/S0022112064001094 · Zbl 0123.22901 · doi:10.1017/S0022112064001094
[10] Hardy, Inequalities (1952)
[11] Peregrine, Waves on Beaches and Resulting Sediment Transport (1972)
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