A Phase Equation of Third-Order in Spatial Derivatives

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Abstract

We derive a phase equation containing terms of third-order in spatial derivatives. In this equation, a nonlinear dissipative term with a third-order derivative suppresses the lowest-order diffusive instability, in cooperation with the other terms of third-order in spatial derivatives. We find an exact shock solution of the phase equation, whose upstream and downstream states are stable, and a periodic solution stable with respect to modulation that is realized through a Hopf bifurcation.

We derive a phase equation containing terms of third-order in spatial derivatives. In this equation, a nonlinear dissipative term with a third-order derivative suppresses the lowest-order diffusive instability, in cooperation with the other terms of third-order in spatial derivatives. We find an exact shock solution of the phase equation, whose upstream and downstream states are stable, and a periodic solution stable with respect to modulation that is realized through a Hopf bifurcation.

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics 107(2), 253-264, 2002-02-25

    THE PHYSICAL SOCIETY OF JAPAN

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  • Lie-Group Approach to Perturbative Renormalization group Method

    GOTO Shin-itiro , MASUTOMI Yuji , NOZAKI Kazuhiro , Department of Physics Nagoya University , Department of Physics Nagoya University , Department of Physics Nagoya University

    Progress of Theoretical Physics 102(3), 471-497, 1999-09-25

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Codes

  • NII Article ID (NAID)
    110001209311
  • NII NACSIS-CAT ID (NCID)
    AA00791455
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    0033068X
  • NDL Article ID
    6087537
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A468
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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