The Lie point symmetry criteria and formation of exact analytical solutions for Kairat-II equation: Paul-Painlevé approach
Faridi W.A. Wazwaz A.-M. Mostafa A.M. Myrzakulov R. Umurzakhova Z.
May 2024Elsevier Ltd
Chaos, Solitons and Fractals
2024#182
The renowned non-linear Kairat-II equation, which expresses the surface curves, is examined meticulously in this work. There has never been a study before that discussed conserved quantities, sensitivity analysis, Hamiltonian function, Lie symmetry invariance criteria, and invariant solutions of Kairat-II equation The Lie invariance criteria are taken into consideration by the symmetry generators. The suggested technique leads to in a four-dimensional Lie algebra, where the translation point symmetries in space and time correlate with the conservation of mass and the energy, respectively, and remaining point symmetries are dilation and scaling. Firstly, we use symmetry reduction of Lie subalgebras to obtain closed-form invariant solutions. In specific reduction cases, we transform the Kairat-II equation into a spectrum of non-linear ordinary differential equations, which have the benefit of being able to offer an extensive selection of closed-form solitary wave solutions. For this equation, the Cauchy problem cannot be solved by the inverse scattering transform, therefore, traveling wave exact solutions are generated using the analytical Paul-Painlevé approach. In both two and three dimensions, the graphical behavior of specific solutions is presented for specific quantities of physical factors of examined equation. Utilizing conservation laws multipliers, the study culminates by determining an extensive set of local conservation laws for the non-linear Kairat-II equation that are applicable to arbitrary constant coefficients. Instead of focusing on the physical aspects of conservation laws, this study computed the conserved quantities using a mathematical perspective that can be used to identify potential symmetries of partial differential equations, guiding readers toward the solutions of partial differential equations. The existence of the Hamiltonian function is presented. The models sensitivity to various starting conditions is highlighted by the sensitivity analysis.
Conserved vectors , Exact solution , Hamiltonian function , Kairat-II equation , Lie analysis , Optimal system , Paul-Painlevé approach
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Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Department of Mathematics, Saint Xavier University, Chicago, 60655, IL, United States
Department of Information Systems, College Computers and Information Science, King Saud University, Riyadh, Saudi Arabia
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, Kazakhstan
Department of Mathematics
Department of Mathematics
Department of Information Systems
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics
10 лет помогаем публиковать статьи Международный издатель
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