We consider the truncated Euler system and analyze bifurcations of a one-front solution to a solution with two fronts. In particular, it is shown that bifurcations of double-humped (single-humped) kink type are caused by perturbations of the upper (lower) critical solution. Bibliography: 2 titles.
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E. A. Lukashov and E. V. Radkevich, “Solidification and structuresation of instability zones,” Appl. Math. 1, No. 3, 159–178 (2010).
E. A. Lukashev, V. V. Palin, E. V. Radkevich, and N. N. Yakovlev, “Nonclassical regularization of the multicomponent Euler system” [in Russian], Probl. Mat. Anal. 73, 67–86 (2013); English transl.: J. Math. Sci., New York 196, No. 3, 322–245 (2014).
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Translated from Problemy Matematicheskogo Analiza 73, October 2013, pp. 125–139.
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Radkevich, E.V. On the Nature of Bifurcations of One-Front Solutions of the Truncated Euler System. J Math Sci 196, 388–404 (2014). https://doi.org/10.1007/s10958-014-1664-y
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DOI: https://doi.org/10.1007/s10958-014-1664-y