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Publication - Dr Tamara Grava

    On the Tritronquée Solutions of (Formula presented.)

    Citation

    Grava, T, Kapaev, A & Klein, C, 2015, ‘On the Tritronquée Solutions of (Formula presented.)’. Constructive Approximation, vol 41., pp. 425-466

    Abstract

    For equation (Formula presented.), the second member in the PI hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $$t$$t and evaluate the asymptotics in the complex x plane for (Formula presented.) and t =o(x<sup>2/3</sup>). Using this result, we identify the most degenerate solutions (Formula presented.), called tritronquée; describe the quasi-linear Stokes phenomenon; and find the large $$n$$n asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronquée solutions.

    Full details in the University publications repository