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Correction to the paper “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”. (English. Russian original) Zbl 1321.35198

Proc. Steklov Inst. Math. 288, 265 (2015); translation from Tr. Mat. Inst. Steklova 288, 287 (2015).
From the text: Unfortunately, some erroneous signs were carried over into [ibid. 281, 161–178 (2013); translation from Tr. Mat. Inst. Steklova 281, 170–187 (2013; Zbl 1293.35279)] from the earlier paper [Russ. J. Math. Phys. 20, No. 2, 155–171 (2013; Zbl 1276.76012)] (see the correction in Russ. J. Math. Phys. 22, No. 1, 144 (2015; Zbl 1321.76011)). The formulas (4.3) and (4.5) should be corrected. In both cases the sign of the second term on the right-hand side was wrong. As a result, the subsequent formulas in the derivation of the transport equation and in the transport equation itself are inaccurate to the same extent. The conclusion on the existence of an anomalous dispersion in this case turns out to be false.
Rapidly oscillating regions of the bottom give rise to effects that are qualitatively similar to those in the case of an ordinary dispersion.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:

[1] Grushin, V. V.; Dobrokhotov, S. Y.u.; Sergeev, S. A., Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source, Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk, 281, 170-187, (2013) · Zbl 1293.35279
[2] Dobrokhotov, S. Y.u.; Sergeev, S. A.; Tirozzi, B., Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients, Russ. J. Math. Phys., 20, 155-171, (2013) · Zbl 1276.76012
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