Advancements in nonlinear dynamics: lie symmetry applications in the jaulent-miodek equation
نویسندگان
1 Northumbria University, Ellison Pl., Newcastle upon Tyne, NE1 8ST Newcastle, United Kingdom.
2 University of Okara, 2 KM Multan Road Renala Khurd By Pass, Okara-Pakistan.
3 Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, Rajasthan, India.
4 Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy.
5 Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India.
doi
10.22105/jarie.2024.469233.1649چکیده
This research presents a detailed analysis of the nonlinear Jaulent-Miodek (J-M) equation through the lens of Lie symmetries. Our primary objective is to comprehensively identify the symmetry group and the optimal systems of Lie sub-algebras pertinent to the J-M equation. We delve into the Lie invariants associated with symmetry generators and demonstrate their contribution to forming similarity-reduced equations that encapsulate the essence of the original equation. Moreover, the study introduces a two-step methodology for establishing the conservation laws relevant to the J-M equation. The initial phase involves identifying suitable multipliers essential for calculating these laws. Subsequently, we utilise symbolic computation to derive these conservation laws formally. This in-depth exploration of the equation’s symmetries and conservation laws not only enhances our understanding of the J-M equation’s intrinsic properties but also aids in simplifying and solving the equation under various conditions.
