A Phase Equation of ThirdOrder in Spatial Derivatives

 Masutomi Yuji MASUTOMI Yuji
 Department of Physics, Nagoya University

 Nozaki Kazuhiro NOZAKI Kazuhiro
 Department of Physics, Nagoya University
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Author(s)

 Masutomi Yuji MASUTOMI Yuji
 Department of Physics, Nagoya University

 Nozaki Kazuhiro NOZAKI Kazuhiro
 Department of Physics, Nagoya University
Abstract
We derive a phase equation containing terms of thirdorder in spatial derivatives. In this equation, a nonlinear dissipative term with a thirdorder derivative suppresses the lowestorder diffusive instability, in cooperation with the other terms of thirdorder 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 thirdorder in spatial derivatives. In this equation, a nonlinear dissipative term with a thirdorder derivative suppresses the lowestorder diffusive instability, in cooperation with the other terms of thirdorder 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), 253264, 20020225
THE PHYSICAL SOCIETY OF JAPAN
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GOTO Shinitiro , 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), 471497, 19990925
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