Radiating solitary waves of a model evolution equation in fluids of finite depth

T. S. Yang; T. R. Akylas

doi:10.1016/0167-2789(95)00058-C

Radiating solitary waves of a model evolution equation in fluids of finite depth

T. S. Yang, T. R. Akylas

Department of Mechanical Engineering

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

8 Citations (Scopus)

Abstract

The evolution equation proposed by Kubota et al. [J. Hydronautics 12 (1978) 157-165] and Joseph [J. Phys. A 10 (1977) 225-227] for long waves in stratified fluids of finite depth is considered. Under a small third-order-derivative dispersive perturbation, solitary-wave solutions to this model equation become weakly nonlocal - they develop oscillatory tails of infinite extent and exponentially small amplitude. Here, these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain.

Original language	English
Pages (from-to)	418-425
Number of pages	8
Journal	Physica D: Nonlinear Phenomena
Volume	82
Issue number	4
DOIs	https://doi.org/10.1016/0167-2789(95)00058-C
Publication status	Published - 1995 May 1

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(95)00058-C

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abstract = "The evolution equation proposed by Kubota et al. [J. Hydronautics 12 (1978) 157-165] and Joseph [J. Phys. A 10 (1977) 225-227] for long waves in stratified fluids of finite depth is considered. Under a small third-order-derivative dispersive perturbation, solitary-wave solutions to this model equation become weakly nonlocal - they develop oscillatory tails of infinite extent and exponentially small amplitude. Here, these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain.",

author = "Yang, {T. S.} and Akylas, {T. R.}",

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AU - Yang, T. S.

AU - Akylas, T. R.

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PY - 1995/5/1

Y1 - 1995/5/1

N2 - The evolution equation proposed by Kubota et al. [J. Hydronautics 12 (1978) 157-165] and Joseph [J. Phys. A 10 (1977) 225-227] for long waves in stratified fluids of finite depth is considered. Under a small third-order-derivative dispersive perturbation, solitary-wave solutions to this model equation become weakly nonlocal - they develop oscillatory tails of infinite extent and exponentially small amplitude. Here, these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain.

AB - The evolution equation proposed by Kubota et al. [J. Hydronautics 12 (1978) 157-165] and Joseph [J. Phys. A 10 (1977) 225-227] for long waves in stratified fluids of finite depth is considered. Under a small third-order-derivative dispersive perturbation, solitary-wave solutions to this model equation become weakly nonlocal - they develop oscillatory tails of infinite extent and exponentially small amplitude. Here, these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain.

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Radiating solitary waves of a model evolution equation in fluids of finite depth

Abstract

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