A MATHEMATICAL JUSTIFICATION OF THE FORCED KORTEWEG-DE VRIES EQUATION FOR CAPILLARY-GRAVITY WAVES

• IGUCHI Tatsuo

  Department of Mathematics Graduate School of Science and Engineering Tokyo Institute of Technology

抄録

The forced Korteweg-de Vries (KdV) equation is the KdV equation with a forcing term and arises as a model for several physical situations. In this paper, we study the validity of this modeling for capillary-gravity waves in an infinitely long canal over an uneven bottom. An underlying background flow of the water together with an uneven bottom causes a deriving force in the KdV equation in some scaling limit. We will show that the solutions of the full problem for capillary-gravity waves split up into two waves moving with different propagation speeds and that the shape of each wave is governed by a forced KdV equation in a slow time scale.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 60 (2), 267-303, 2006

  九州大学大学院数理学研究院

キーワード

• capillary-gravity waves
• forced KdV equation
• long-wave approximation

詳細情報

• CRID: 1390001205230016128
• NII論文ID: 130000063141
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.60.267
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2268237
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/60/2/60_2_267/_pdf
• 本文言語コード: en
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