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

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 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].

• Keywords

Meromorphic solutions Cubic-Quintic Swift-Hohenberg equation Nevanlinna theory

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@Article{ATA-30-108, author = {C. F. Wu}, 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 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].}, 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 AU - C. F. Wu JO - Analysis in Theory and Applications VL - 1 SP - 108 EP - 119 PY - 2014 DA - 2014/03 SN - 30 DO - http://dor.org/10.4208/ata.2014.v30.n1.7 UR - https://global-sci.org/intro/ata/4476.html KW - Meromorphic solutions KW - Cubic-Quintic Swift-Hohenberg equation KW - 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 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].