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Abstract: The multiple scale expansion method is used to derive amplitude equations fora system with thermohaline convection in the neighborhood of Hopf and Taylorbifurcation points and at the double zero point of the dispersion relation. Acomplex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and anequation of the $\phi^4$ type, respectively, were obtained. Analyticexpressions for the coefficients of these equations and their variousasymptotic forms are presented. In the case of Hopf bifurcation for low andhigh frequencies, the amplitude equation reduces to a perturbed nonlinearSchr\-odinger equation. In the high-frequency limit, structures of the type of-dark- solitons are characteristic of the examined physical system.



Author: S. B. Kozitskiy

Source: https://arxiv.org/



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