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Investigation of Chaotic Phenomena by a Soliton Lattice Model

Research Project

Project/Area Number 63540287
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

KAWAHARA Takuji  Kyoto Univ., Fac.Sci. Associate Prof., 理学部, 助教授 (60027373)

Co-Investigator(Kenkyū-buntansha) TOH Sadayoshi  Kyoto Univ., Fac.Sci. Research Assoc., 理学部, 助手 (10217458)
Project Period (FY) 1988 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1989: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1988: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordschaos / soliton / soliton lattice model / nonlinear evolution equation / spatially localized structure / pulse interaction / nonlinear lattice oscillation / cylindrically symmetric solitary wave / 軸対称孤立波
Research Abstract

The purpose of this research is to describe a variety of "soliton" or "chaos" phenomena arising in certain nonlinear evolution equations by means of a superposition of spatially localized structures. A soliton lattice model which approximates solutions of an evolution equation with instability, dissipation and dispersion is proposed to investigate the properties of chaotic behaviors. The idea is applied extensively to several dissipative-dispersive equations in one- or two-space dimension and also to descriptions of strong chaos. The obtained results are summarized as follows.
1. Chaotic behaviors in dispersive or dissipative systems are discussed in relation to symmetric or asymmetric oscillatory soliton lattice model. The finding is that an asymmetry in lattice is associated with non-conservative property and interactions of more than 3 pulses with oscillatory tail structure introduce irregularities in the motion.
2. Solutions of the unstable KdV-Burgers equation show chaotic behaviors … More for strongly dispersive case. Stationary shock structures develop for strongly dissipative case in consistent with the dispersion relation for this equation. Spectra of chaos in the Ginzburg-Landau equation are described theoretically by a superposition of exact envelope soliton solutions, which provides a satisfactory lowest approximation to numerically obtained spectra.
3. Two-dimensional dissipative-dispersive equation is solved numerically to show that one-dimensional solutions are generally unstable and two-dimensionally localized structures are generated. For weakly dispersive case, overall behaviors are chaotic, while, for strongly dispersive case, two-dimensionally localized pulse structures develop and they relax into a "quasi-lattice" arrangement in two-dimensional space.
4. It is found numerically that cylindrically symmetric solitary waves become fundamental to the Zakharov-Kuznetsov equation. This solitary wave travels stably when isolated, but behaves as "quasi-soliton" in case of collision, because changes in amplitude and generations of ripple take place during collisions. Less

Report

(3 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • Research Products

    (40 results)

All Other

All Publications (40 results)

  • [Publications] T.Kawahara: "Pulse interaction and wave evolutions in an unstable dissipative dispersive system." Proc.IUTAM Symposium on Non-Linear Water Waves.190-198 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Pulse interactions in an unstable dissipative-dispersive nonlinear system." Phys.Fluids. 31-8. 2103-2111 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Chaotic motions in an oscillatory soliton lattice." J.Phys.Soc.Japan. 57-11. 3714-3732 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "On some properties of solutions to a nonlinear evolution equation including long wavelength instability." Contributions to Nonlinear Wave Motion.95-117 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 川原琢治: "液膜流における2次元パルス" 京都大学数理解析研究所講究録ソリトン理論における広田の方法. 684. 233-252 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Chaotic behaviour of soliton lattice in an unstable dissipative dispersive nonlinear system." Physica D. 39. 43-58 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] S.Toh: "Two-dimensionally localized pulses of a nonlinear equation with dissipation and dispersion." Phys.Rev.A. 40-9. 5472-5475 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] H.Iwasaki: "Cylindrical guasi-solitons of the Zakharov-Kuznetsov equation." Physica D. (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 川原琢治: "ソリトンからカオスへ" 物性研究. 54. 1-12 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 川原琢治: "物理学最前線22ソリトンとカオス" 共立出版, 69 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 川原琢治: "流体における波動第1章(分担執筆)" 朝倉書店, 52 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara, S.Toh & M.Takaoka: "Pulse interaction and wave evolutions in an unstable dissipative dispersive system." Proc. IUTAM Symp. 190-198, (1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara & S.Toh: "Pulse interactions in an unstable dissipative-dispersive nonlinear system." Phys.Fluids, 31-8, 2103-2111, (1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara & M.Takaoka: "Chaotic motions in an oscillatory soliton lattice." J.Phys.Soc.Japan, 57-11, 3714-3732, (1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara & S.Toh: "On some properties of solutions to a nonlinear evolution equation including long wavelength instability." Contributions to Nonlinear Wave Motion, 95-117, (1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara, S.Toh & H.Iwasaki: "Two-dimensional pulse in liquid film flow." RIMS 684, 233-252, (1989).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara & M.Takaoka: "Chaotic behavior of soliton lattice in an unstable dissipative dispersive non-linear system." Physica D39, 43-58, (1989).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] S.Toh, H.Iwasaki & T.Kawahara: "Two-dimensionally localized pulses of a nonlinear equation with dissipation and dispersion." Phys.Rev.A, 40-9, 5472-5475, (1989).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] H.Iwasaki, S.Toh & T.Kawahara: "Cylindrical quasisolitons of the Zakharov-Kuznetsov equation." Physica D (1990).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "From soliton to chaos." Bussei Kenkyu, 1-12, (1990).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Soliton and chaos." Kyoritsu Shuppan, 1-69, (1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Waves in fluids." Asakura, 1-52, (1989).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Kawahara: "Pulse interaction and wave elolutions in an unstable dissipative dispersive system." Proc.IUTAM Symposium on NonーLinear Water Waves.190-198 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Kawahara: "Pulse interactions in an unstable dissipative-dispersive nonlinear system." Phys.Fluids. 31ー8. 2103-2111 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Kawahara: "Chaotic motions in an oscillatry soliton lattice." J.Phys.Soc.Japan. 57ー11. 3714-3732 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Kawahara: "On some properties of solutions to a nonlinear evolution equation including long wavelength instability." Contributions to Nonlinear Wave Motion.95-117 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] 川原琢治: "液膜流における2次元パルス" 京都大学数理解析研究所講究録,ソリトン理論における広田の方法. 684. 233-252 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Kawahara: "Chaotic behaviour of soliton lattice in an unstable dissipative dispersive nonlinear system." Physica D. 39. 43-58 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] S.Toh: "Twoーdimensionally localized pulses of a nonlinear equation with dissipation and dispersion" Phys.Rev.A. 40ー9. 5472-5475 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] H.Iwasaki: "Cylindrical quasiーsolitons of the ZakharovーKuznetsov equation." Physica D. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 川原琢治: "ソリトンからカオスへ" 物性研究. 54. 1-12 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 川原琢治: "物理学最前線22,ソリトンとカオス" 共立出版, 69 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] 川原琢治: "流体における波動,第1章 (分担執筆)" 朝倉書店, 52 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Kawahara: Proc.IUTAM Symposium on Nonlinear Water Waves. 190-198 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Kawahara: Phys.Fluids. 31. 2103-2111 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Kawahara: J.Phys.Soc.Japan. 57. 3714-3732 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Kawahara: Nonlinear Wave Motion(Longman Scientific & Technical). 95-117 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 川原琢治: 京都大学数理解析研究所講究録「ソリトン理論における広田の方法」研究会. 1-20 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Kawahara: Physica D. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 川原琢治: "物理学最前線22「ソリトンとカオス」" 共立出版, 1-69 (1988)

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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