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Zh. Mat. Fiz. Anal. Geom., 2006, Volume 2, Number 3, Pages 278–286 (Mi jmag35)  

This article is cited in 21 scientific papers (total in 21 papers)

Meromorphic traveling wave solutions of the Kuramoto–Sivashinsky equation

Alexandre Eremenko

Purdue University, 150 N University Str., West Lafayette IN 47907-2067, USA

Key words and phrases: Kuramoto and Sivashinsky equation, meromorphic functions, elliptic functions, Nevanlinna theory.

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Document Type: Article
MSC: 35Q20, 34A20
Received: 13.09.2005
Language: English

Citation: Alexandre Eremenko, “Meromorphic traveling wave solutions of the Kuramoto–Sivashinsky equation”, Zh. Mat. Fiz. Anal. Geom., 2:3 (2006), 278–286

Citation in format AMSBIB
\by Alexandre Eremenko
\paper Meromorphic traveling wave solutions of the Kuramoto--Sivashinsky equation
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2006
\vol 2
\issue 3
\pages 278--286

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    This publication is cited in the following articles:
    1. Kudryashov N.A., Soukharev M.B., “Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation”, Regul. Chaotic Dyn., 14:3 (2009), 407–419  crossref  mathscinet  zmath  isi  elib
    2. Eremenko A.E., Liangwen L. and Tuen W.N., “Meromorphic solutions of higher order Briot-Bouquet differential equations”, Math. Proc. Camb. Philos. Soc., 146:1 (2009), 197–206  crossref  mathscinet  zmath  isi
    3. Conte R., Ng Tuen-Wai, “Meromorphic solutions of a third order nonlinear differential equation”, J. Math. Phys., 51 (2010), 033518, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Kudryashov N.A., “Meromorphic solutions of nonlinear ordinary differential equations”, Commun. Nonlinear Sci. Numer. Simul., 15:10 (2010), 2778–2790  crossref  mathscinet  zmath  isi  elib
    5. Demina M.V., Kudryashov N.A., “From Laurent series to exact meromorphic solutions: The Kawahara equation”, Phys. Lett. A, 374:39 (2010), 4023–4029  crossref  mathscinet  zmath  isi  elib
    6. Demina M.V., Kudryashov N.A., “Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations”, Commun. Nonlinear Sci. Numer. Simul., 16:3 (2011), 1127–1134  crossref  mathscinet  zmath  isi  elib
    7. Kudryashov N.A., Sinelshchikov D.I., Demina M.V., “Exact solutions of the generalized Bretherton equation”, Phys. Lett. A, 375:7 (2011), 1074–1079  crossref  mathscinet  zmath  isi  elib
    8. Kamenov O.Y., “Periodic solutions of the non-integrable convective fluid equation”, J. Math. Phys., 53:6 (2012), 063705  crossref  mathscinet  zmath  isi
    9. Conte R., Ng T.-W., “Meromorphic Traveling Wave Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation”, Acta Appl. Math., 122:1, SI (2012), 153–166  crossref  zmath  isi  scopus
    10. Conte R., Ng T.-W., Wong K.-K., “Exact Meromorphic Stationary Solutions of the Real Cubic Swift-Hohenberg Equation”, Stud. Appl. Math., 129:1 (2012), 117–131  crossref  zmath  isi  scopus
    11. Kao H.-Ch., Knobloch E., “Exact Solutions of the Cubic-Quintic Swift-Hohenberg Equation and Their Bifurcations”, Dynam. Syst., 28:2 (2013), 263–286  crossref  zmath  isi  scopus
    12. Huang Z., Zhang L., Chen Q., Yuan W., “the Representation of Meromorphic Solutions For a Class of Odd Order Algebraic Differential Equations and Its Applications”, Math. Meth. Appl. Sci., 37:10 (2014), 1553–1560  crossref  mathscinet  zmath  isi
    13. Yuan W., Li Y., Qi J., “All Meromorphic Solutions of Some Algebraic Differential Equations and Their Applications”, Adv. Differ. Equ., 2014, 105  crossref  mathscinet  isi
    14. Demina M.V., Kudryashov N.A., “Elliptic Solutions in the Henon-Heiles Model”, Commun. Nonlinear Sci. Numer. Simul., 19:3 (2014), 471–482  crossref  mathscinet  isi  elib
    15. Gallagher P.X., “Some Algebraic Differential Equations With Few Transcendental Solutions”, J. Math. Anal. Appl., 428:2 (2015), 717–734  crossref  mathscinet  zmath  isi
    16. Halburd R., Wang J., “All Admissible Meromorphic Solutions of Hayman'S Equation”, Int. Math. Res. Notices, 2015, no. 18, 8890–8902  crossref  mathscinet  zmath  isi
    17. Zhang Yu., Gao Z., Zhang J., “All Admissible Meromorphic Solutions of Certain Type of Second Degree Second Order Algebraic ODEs”, J. Math. Anal. Appl., 452:2 (2017), 1182–1193  crossref  mathscinet  zmath  isi  scopus
    18. Chen Sh., Lin W., “Periodicity and Uniqueness of Meromorphic Functions Concerning Sharing Values”, Houst. J. Math., 43:3 (2017), 763–781  mathscinet  zmath  isi
    19. Demina M.V., Kudryashov N.A., “Meromorphic Solutions in the Fitzhugh-Nagumo Model”, Appl. Math. Lett., 82 (2018), 18–23  crossref  zmath  isi  scopus
    20. Demina M.V., “Novel Algebraic Aspects of Liouvillian Integrability For Two-Dimensional Polynomial Dynamical Systems”, Phys. Lett. A, 382:20 (2018), 1353–1360  crossref  zmath  isi  scopus
    21. Gu Y., Deng B., Lin J., “Exact Traveling Wave Solutions to the (2+1)-Dimensional Jaulent-Miodek Equation”, Adv. Math. Phys., 2018, 5971646  crossref  isi  scopus
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