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

C. F. Wu

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

Published online: 2014-03

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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 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].

  • AMS Subject Headings

35Q53

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COPYRIGHT: © Global Science Press

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@Article{ATA-30-108, author = {}, title = {Exact Meromorphic Stationary Solutions of the Cubic-Quintic Swift-Hohenberg Equation}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {1}, pages = {108--119}, 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 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].

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n1.7}, url = {http://global-sci.org/intro/article_detail/ata/4476.html} }
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 -

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 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].

C. F. Wu. (1970). Exact Meromorphic Stationary Solutions of the Cubic-Quintic Swift-Hohenberg Equation. Analysis in Theory and Applications. 30 (1). 108-119. doi:10.4208/ata.2014.v30.n1.7
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