TY - JOUR
T1 - Exact Meromorphic Stationary Solutions of the Cubic-Quintic Swift-Hohenberg Equation
JO - Analysis in Theory and Applications
VL - 1
SP - 108
EP - 119
PY - 2014
DA - 2014/03
SN - 30
DO - http://doi.org/10.4208/ata.2014.v30.n1.7
UR - https://global-sci.org/intro/article_detail/ata/4476.html
KW - Meromorphic solutions, Cubic-Quintic Swift-Hohenberg equation, Nevanlinna theory.
AB - <p style="text-align: justify;">In this paper, we study an ODE of the form$$b_0 u^{(4)} + b_1 u&#39;&#39; + b_2 u + b_3 u^3 + b_4 u^5 = 0, \&nbsp; &#39; = \frac{d}{d z},$$ which includes, as a special case, &nbsp;the stationary case of the cubic-quintic Swift-Hohenberg equation. Based on Nevanlinna theory and Painlevé 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].</p>