On the generalized reduced Ostrovsky equation

Nakao Hayashi; Pavel I. Naumkin

On the generalized reduced Ostrovsky equation

Research output: Contribution to journal › Article › peer-review

Abstract

We survey recent progress on the case of the Cauchy problem for the generalized reduced Ostrovsky equation u_t = S (∂_x) u + (f (u))_x, where the operator S (∂_x) is defined through the Fourier transform as (Formula Presented.), and the nonlinear interaction is given by (Formula Presented.) if ρ > 1 is not an integer and f (u) = u^ρ-1 if ρ > 1 is an integer.

Original language	English
Pages (from-to)	67-101
Number of pages	35
Journal	SUT Journal of Mathematics
Volume	50
Issue number	2
Publication status	Published - 2014
Externally published	Yes

Keywords

Asymptotic behavior of solutions
Nonexistence of scattering states
Reduced Ostrovsky

ASJC Scopus subject areas

Mathematics(all)

Cite this

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AB - We survey recent progress on the case of the Cauchy problem for the generalized reduced Ostrovsky equation ut = S (∂x) u + (f (u))x, where the operator S (∂x) is defined through the Fourier transform as (Formula Presented.), and the nonlinear interaction is given by (Formula Presented.) if ρ > 1 is not an integer and f (u) = uρ-1 if ρ > 1 is an integer.

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KW - Nonexistence of scattering states

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On the generalized reduced Ostrovsky equation

Abstract

Keywords

ASJC Scopus subject areas

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