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Positive periodic solutions to a nonlinear fourth-order differential equation
Bifurcation and stability of the generalized complex Ginzburg--Landau equation
1. | Department of Mathematics, New York Institute of Technology, Old Westbury, NY 11568, United States |
[1] |
Simão Correia, Mário Figueira. A generalized complex Ginzburg-Landau equation: Global existence and stability results. Communications on Pure and Applied Analysis, 2021, 20 (5) : 2021-2038. doi: 10.3934/cpaa.2021056 |
[2] |
Rui Dilão, András Volford. Excitability in a model with a saddle-node homoclinic bifurcation. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 419-434. doi: 10.3934/dcdsb.2004.4.419 |
[3] |
Ping Liu, Junping Shi, Yuwen Wang. A double saddle-node bifurcation theorem. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2923-2933. doi: 10.3934/cpaa.2013.12.2923 |
[4] |
Satoshi Kosugi, Yoshihisa Morita, Shoji Yotsutani. A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions. Communications on Pure and Applied Analysis, 2005, 4 (3) : 665-682. doi: 10.3934/cpaa.2005.4.665 |
[5] |
Flaviano Battelli. Saddle-node bifurcation of homoclinic orbits in singular systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 203-218. doi: 10.3934/dcds.2001.7.203 |
[6] |
Kie Van Ivanky Saputra, Lennaert van Veen, Gilles Reinout Willem Quispel. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 233-250. doi: 10.3934/dcdsb.2010.14.233 |
[7] |
Qiongwei Huang, Jiashi Tang. Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 129-141. doi: 10.3934/dcdsb.2010.14.129 |
[8] |
Shujuan Lü, Chunbiao Gan, Baohua Wang, Linning Qian, Meisheng Li. Traveling wave solutions and its stability for 3D Ginzburg-Landau type equation. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 507-527. doi: 10.3934/dcdsb.2011.16.507 |
[9] |
Noboru Okazawa, Tomomi Yokota. Smoothing effect for generalized complex Ginzburg-Landau equations in unbounded domains. Conference Publications, 2001, 2001 (Special) : 280-288. doi: 10.3934/proc.2001.2001.280 |
[10] |
Majid Gazor, Mojtaba Moazeni. Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 205-224. doi: 10.3934/dcds.2015.35.205 |
[11] |
N. Maaroufi. Topological entropy by unit length for the Ginzburg-Landau equation on the line. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 647-662. doi: 10.3934/dcds.2014.34.647 |
[12] |
Hans G. Kaper, Peter Takáč. Bifurcating vortex solutions of the complex Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 871-880. doi: 10.3934/dcds.1999.5.871 |
[13] |
Jingna Li, Li Xia. The Fractional Ginzburg-Landau equation with distributional initial data. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2173-2187. doi: 10.3934/cpaa.2013.12.2173 |
[14] |
Jun Yang. Vortex structures for Klein-Gordon equation with Ginzburg-Landau nonlinearity. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2359-2388. doi: 10.3934/dcds.2014.34.2359 |
[15] |
Noboru Okazawa, Tomomi Yokota. Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 311-341. doi: 10.3934/dcds.2010.28.311 |
[16] |
Sen-Zhong Huang, Peter Takáč. Global smooth solutions of the complex Ginzburg-Landau equation and their dynamical properties. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 825-848. doi: 10.3934/dcds.1999.5.825 |
[17] |
Francisco Guillén-González, Mouhamadou Samsidy Goudiaby. Stability and convergence at infinite time of several fully discrete schemes for a Ginzburg-Landau model for nematic liquid crystal flows. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4229-4246. doi: 10.3934/dcds.2012.32.4229 |
[18] |
Yan Zheng, Jianhua Huang. Exponential convergence for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5621-5632. doi: 10.3934/dcdsb.2019075 |
[19] |
Hongzi Cong, Jianjun Liu, Xiaoping Yuan. Quasi-periodic solutions for complex Ginzburg-Landau equation of nonlinearity $|u|^{2p}u$. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 579-600. doi: 10.3934/dcdss.2010.3.579 |
[20] |
Michael Stich, Carsten Beta. Standing waves in a complex Ginzburg-Landau equation with time-delay feedback. Conference Publications, 2011, 2011 (Special) : 1329-1334. doi: 10.3934/proc.2011.2011.1329 |
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