USING THE JACOBI LAST MULTIPLIER APPROACH TO LINEARIZE THE MATHEW-LAKSHMANAN OSCILLATOR EQUATION - Orverem, Joel Mvendaga (FUDMA Journal of Sciences, 2025)
The Mathews–Lakshmanan (ML) oscillator is a remarkable nonlinear dynamical system that preserves several features of the linear harmonic oscillator while exhibiting inherent nonlinearity. Owing to its exact solvability, linearizability, and relevance in classical and quantum mechanics, the ML oscillator has attracted significant research interest across physics, engineering, and applied mathematics. Parallel to this, the Jacobi Last Multiplier (JLM) method originally developed by Carl Gustav Jacobi has re-emerged as a powerful analytical tool for deriving Lagrangians, identifying first integrals, and revealing variational structures of nonlinear differential equations. In this study, we apply the JLM framework to the ML oscillator in order to construct its corresponding Lagrangian and perform an explicit linearization.
Keywords: Linearization; Mathew-Lakshmanan Oscillator Equation; Differential Equation; Jacobi Last Multiplier