Volume 30, Issue 1
Exact Meromorphic Stationary Solutions of the Cubic-Quintic Swift-Hohenberg Equation

C. F. Wu

10.4208/ata.2014.v30.n1.7

Anal. Theory Appl., 30 (2014), pp. 108-119

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  • Abstract

In this paper, we study an ODE of the form$$b_0 u^{(4)} + b_1 u'' + b_2 u + b_3 u^3 + b_4 u^5 = 0, ' = \frac{d}{d z},$$ which includes, as a special case, the stationary case of the cubic-quintic Swift-Hohenberg equation.Based on Nevanlinna theory and Painlev\'{e} analysis, we first show that all its meromorphic solutions are elliptic or degenerate elliptic. Then we obtain them all explicitly by the method introduced in [7].

  • History

Published online: 2014-03

  • AMS Subject Headings

35Q53

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