Abstract:
Some methods to look for exact solutions of nonlinear differential equations are discussed. It is shown that many popular methods are equivalent to each other. Several recent publications with "new" solitary wave solutions for the Kuramoto–Sivashinsky equation are analyzed. We demonstrate that all these solutions coincide with the known ones.
Citation:
N. A. Kudryashov, M. B. Soukharev, “Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation”, Regul. Chaotic Dyn., 14:3 (2009), 407–419
\Bibitem{KudSou09}
\by N. A. Kudryashov, M. B. Soukharev
\paper Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 3
\pages 407--419
\mathnet{http://mi.mathnet.ru/rcd589}
\crossref{https://doi.org/10.1134/S1560354709030046}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2525621}
\zmath{https://zbmath.org/?q=an:1229.34008}
Linking options:
https://www.mathnet.ru/eng/rcd589
https://www.mathnet.ru/eng/rcd/v14/i3/p407
This publication is cited in the following 53 articles:
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Akhtar Hussain, Hassan Ali, M. Usman, F. D. Zaman, Choonkil Park, M. M. Bhatti, “Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models”, Journal of Mathematics, 2024 (2024), 1
Reem K. Alhefthi, Kalim U. Tariq, Ahmet Bekir, Arslan Ahmed, “On some novel solitonic structures for the Zhiber–Shabat model in modern physics”, Zeitschrift für Naturforschung A, 2024
YANZHI MA, ZENGGUI WANG, “BIFURCATION AND EXACT SOLUTIONS OF SPACE-TIME FRACTIONAL SIMPLIFIED MODIFIED CAMASSA–HOLM EQUATION”, Fractals, 31:07 (2023)
M. Mossa Al-Sawalha, Humaira Yasmin, Rasool Shah, Abdul Hamid Ganie, Khaled Moaddy, “Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation”, Fractal Fract, 7:10 (2023), 753
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sophiya F. Lavrova, Dariya V. Safonova, “On solutions of one of the second-order nonlinear differential equation: An in-depth look and critical review”, Optik, 255 (2022), 168674
S. A. El-Tantawy, L. S. El-Sherif, A. M. Bakry, Weaam Alhejaili, Abdul-Majid Wazwaz, “On the analytical approximations to the nonplanar damped Kawahara equation: Cnoidal and solitary waves and their energy”, Physics of Fluids, 34:11 (2022)
Sahar Albosaily, Wael W. Mohammed, Ali Rezaiguia, Mahmoud El-Morshedy, Elsayed M. Elsayed, “The influence of the noise on the exact solutions of a Kuramoto-Sivashinsky equation”, Open Mathematics, 20:1 (2022), 108
Wael W. Mohammed, A. M. Albalahi, S. Albadrani, E. S. Aly, R Sidaoui, A. E. Matouk, A. M. Nagy, “The Analytical Solutions of the Stochastic Fractional Kuramoto–Sivashinsky Equation by Using the Riccati Equation Method”, Mathematical Problems in Engineering, 2022 (2022), 1
Mohammed W.W. Alesemi M. Albosaily S. Iqbal N. El-Morshedy M., “The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation By Using (G `/G)-Expansion Method”, Mathematics, 9:21 (2021), 2712
Seadawy A.R., Ali A., Helal M.A., “Analytical Wave Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli and Boiti-Leon-Manna-Pempinelli Equations By Mathematical Methods”, Math. Meth. Appl. Sci., 44:18 (2021), 14292–14315
Seadawy A.R., Ali A., Althobaiti S., Sayed S., “Propagation of Wave Solutions of Nonlinear Heisenberg Ferromagnetic Spin Chain and Vakhnenko Dynamical Equations Arising in Nonlinear Water Wave Models”, Chaos Solitons Fractals, 146 (2021), 110629
Kudryashov N.A., “The Radhakrishnan-Kundu-Lakshmanan Equation With Arbitrary Refractive Index and Its Exact Solutions”, Optik, 238 (2021), 166738
Kudryashov N.A., “Optical Solitons of the Resonant Nonlinear Schrodinger Equation With Arbitrary Index”, Optik, 235 (2021), 166626
Nikolay A. Kudryashov, “Model of propagation pulses in an optical fiber with a new law of refractive indices”, Optik, 248 (2021), 168160
Ali A., Seadawy A.R., Baleanu D., “Propagation of Harmonic Waves in a Cylindrical Rod Via Generalized Pochhammer-Chree Dynamical Wave Equation”, Results Phys., 17 (2020), 103039
Seadawy A.R., Ali A., Albarakati W.A., “Analytical Wave Solutions of the (2”, Results Phys., 15 (2019), 102775
Tchaho Clovis Taki Djeumen, Omanda H.M., Mbourou Gaston N'tchayi, Bogning J.R., Kofane T.C., “Multi-Form Solitary Wave Solutions of the Kdv-Burgers-Kuramoto Equation”, J. Phys. Commun., 3:10 (2019), UNSP 105013
Ahmed I., Seadawy A.R., Lu D., “Rogue Waves Generation and Interaction of Multipeak Rational Solitons in the System of Equations For the Ion Sound and Langmuir Waves”, Int. J. Mod. Phys. B, 33:24 (2019), 1950277
Kabir M.M., “Exact Traveling Wave Solutions For Nonlinear Elastic Rod Equation”, J. King Saud Univ. Sci., 31:3 (2019), 390–397
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