Equivalence transformations of families of quasi-linear elliptic equations of the second order of a function of two variables
https://doi.org/10.29235/1561-2430-2026-62-1-27-37
Анатацыя
In this work, we search for infinitesimal equivalence transformations of 16 families of quasi-linear elliptic equations of the second order in two variables. A symmetry reduction has been performed for the families of equations utt + uxx = f(t,x,u), utt + uxx = f(x,u).
Аб аўтары
D. S. Zhalukevich
Institute of Mathematics of the National Academy of Sciences of Belarus
Беларусь
Беларусь
Dzianis S. Zhalukevich – Applicant, Department of
Differential Equations
11, Surganov Str., 220072, Minsk
Спіс літаратуры
1. Zhalukevich, D. S. Equivalence transformations of families of second-order quasi-linear hyperbolic equations of two variables / D. S. Zhalukevich // Arxiv [Preprint] – 2025. – URL: https://www.researchgate.net/publication/398918025_Equivalence_transformations_of_families_of_second-order_quasi-linear_hyperbolic_equations_of_two_variables.
2. Zhalukevich, D. S. Reduction of nonlinear Klein-Gordon equations for a function of two variables / D. S. Zhalukevich // Arxiv [Preprint] – 2025. – URL: https://www.researchgate.net/publication/399149445_Reduction_of_nonlinear_KleinGordon_equations_for_a_function_of_two_variables
3. Lahno, V. Group classification of quasilinear elliptic-type equations. I. Invariance with respect to Lie algebras with nontrivial Levi decomposition / V. Lahno, S. V. Spichak // Ukrainian Mathematical Journal. – 2007. – Vol. 59. – P. 1719–1736. https://doi.org/10.1007/s11253-008-0021-z
4. Lahno, V. Group classification of quasilinear elliptic-type equations. II. Invariance under solvable Lie algebras / V. Lahno, S. V. Spichak // Ukrainian Mathematical Journal. – 2011. – Vol. 63. – P. 236–253. https://doi.org/10.1007/s11253-011-0501-4
5. Torrisi, M. On equivalence transformations applied to a non-linear wave equation / M. Torrisi, R. Tracina, A. Valenti // Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. – Netherlands, Kluwer Academic Publishers, 1993. – P. 367–375. https://doi.org/10.1007/978-94-011-2050-0_39
6. Tracina, R. Invariants of a family of nonlinear wave equations / R. Tracina // Communications in Nonlinear Science and Numerical Simulation. – 2004. – Vol. 9, № 1. – P. 127–133. https://doi.org/10.1016/S1007-5704(03)00021-2
7. Torrisi, M. On the linearization of semilinear wave equations / M. Torrisi, R. Tracina, A. Valenti // Nonlinear Dynamics. – 2004. – Vol. 36. – P. 97–106. https://doi.org/10.1023/b:nody.0000034649.74389.09
8. Boyko, V. M. Realizations of Lie algebras on the line and the new group classification of (1 + 1)-dimensional generalized nonlinear Klein – Gordon equations / V. M. Boyko, O. V. Lokaziuk, R. O. Popovych // Journal of Mathematical Physics. – 2021. – Vol. 11. – Art. ID 127. https://doi.org/10.1007/s13324-021-00550-z
9. Lahno, V. The Group Classification of One Class of Nonlinear Wave Equations / V. Lahno, O. Magda // Arxiv [Preprint]. – 2003. – URL: https://arxiv.org/abs/math-ph/0310049; https://doi.org/10.48550/arXiv.math-ph/0310049
10. Lahno, V. Group classification of nonlinear wave equations / V. Lahno, R. Zhdanov // Journal of Mathematical Physics. – 2005. – Vol. 46, № 5. – Art. 053301. https://doi.org/10.1063/1.1884886
11. Lahno, V. Group classification and exact solutions of nonlinear wave equations / V. Lahno, R. Zhdanov, O. Magda // Acta Applicandae Mathematicae. – 2006. – Vol. 91. – P. 253–313 https://doi.org/10.1007/s10440-006-9039-0
12. Popovych, R. O. Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations / R. O. Popovych // Applied Mathematics Letters. – 2021. – Vol. 116. – Art. ID 107068. https://doi.org/10.1016/j.aml.2021.107068
13. Lie, S. Diskussion der Dierentialgleichung d2 z/dxdy = F(z) / S. Lie // Archiv for Mathematik og Naturvidenskab. – 1881. – Vol. 5. – P. 282–306.
14. Pucci, E. Group properties of a class of semilinear hyperbolic equations / E. Pucci, M. C. Salvatori // International Journal of Non-Linear Mechanics. – 1986. – Vol. 21, № 2. – P. 147–155. https://doi.org//10.1016/0020-7462(86)90027-2
15. Azad, H. Group classification, optimal system and optimal reductions of a class of Klein Gordon equations / H. Azad, M. T. Mustafa, M. Ziad // Communications in Nonlinear Science and Numerical Simulation. – 2010. – Vol. 15, № 5. – P. 1132– 1147. https://doi.org/10.1016/j.cnsns.2009.05.045
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