Abstract
The paper presents the results of the symmetry classification of nonlinear integrable 2-field evolutionary systems of the third order with a constant separant.
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REFERENCES
V. G. Drinfeld and V. V. Sokolov, “New evolution equations having (L, A) pairs,” Tr. Sem. S.L. Soboleva, Inst. Mat., Novosibirsk 2, 5–9 (1981).
M. V. Foursov, “Towards the complete classification of homogeneous two-component integrable equations,” J. Math. Phys. 44, 3088–3096 (2003).
D. S. Wang, “Complete integrability and the Miura transformation of a coupled KdV equation,” Appl. Math. Lett. 23, 665–669 (2010).
D. S. Wang, J. Liu, and Z. Zhang, “Integrability and equivalence relationships of six integrable coupled Korteweg–de Vries equations,” Math. Methods Appl. Sci. 36 (12), 3516–3530 (2016).
A. G. Meshkov, “Necessary conditions of the integrability,” Inverse Probl. 10 (3), 635–653 (1994).
A. G. Meshkov and I. V. Kulemin, “To the classification of integrable systems in 1+1 dimensions,” Proceedings of the 2nd International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv, Ukraine, July 7–13, 1997 (1997), pp. 115–121.
A. G. Meshkov and V. V. Sokolov, “Integrable evolution equations on the N-dimensional sphere,” Commun. Math. Phys. 232 (1), 1–18 (2002).
M. Yu. Balakhnev, “A class of integrable evolutionary vector equations,” Theor. Math. Phys. 142 (1), 8–14 (2005).
M. Ju. Balakhnev and A. G. Meshkov, “Integrable anisotropic evolution equations on a sphere,” SIGMA 1, 027 (2005). nlin.SI/0512032
A. G. Meshkov, “Symmetry classification of divergent evolution systems of the third order,” Fundam. Prikl. Mat. 12 (7), 141–161 (2006).
A. G. Meshkov and M. Ju. Balakhnev, “Two-field integrable evolutionary systems of the third order and their differential substitutions,” Symmetry, Integrability, Geom.: Methods Appl. 4, 018 (2008).
A. G. Meshkov and V. V. Sokolov, “Integrable evolution equations with a constant separant,” Ufim. Mat. Zh. 4 (3), 104–154 (2012).
ACKNOWLEDGMENTS
I am grateful to Prof. A.G. Meshkov for stating the problem, providing the Jet package for the symmetry analysis of evolutionary equations and systems, and for useful recommendations in the course of calculations.
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Translated by E. Chernokozhin
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Balakhnev, M.Y. Results of Symmetry Classification of 2-Field Third-Order Evolutionary Systems with a Constant Separant. Comput. Math. and Math. Phys. 63, 564–581 (2023). https://doi.org/10.1134/S0965542523040048
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DOI: https://doi.org/10.1134/S0965542523040048