A Phase Equation of Third-Order in Spatial Derivatives | Zendy

Yuji Masutomi | Zendy; Kazuhiro Nozaki | Zendy

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A Phase Equation of Third-Order in Spatial Derivatives

Author(s) -

Yuji Masutomi,

Kazuhiro Nozaki

Publication year - 2002

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.107.253

Subject(s) - third order , physics , dissipative system , instability , hopf bifurcation , phase (matter) , order (exchange) , nonlinear system , bifurcation , mathematical analysis , mathematical physics , quantum mechanics , mathematics , law , finance , economics , political science

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 lowestorder 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.

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