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<p>The logarithmic modified nonlinear Schrödinger equation (LMNLSE) extends the classical nonlinear Schrödinger equation by incorporating a logarithmic nonlinearity to account for specific quantum effects and wave phenomena. This study examines the symmetry structure of the LMNLSE using the Lie symmetry (LS) method. By systematically identifying the LSs of the equation, invariant solutions are obtained, enhancing the understanding of its underlying dynamics. Furthermore, the conservation laws associated with the LMNLSE are explored through the application of Ibragimov’s theorem, utilizing symmetries to obtain conserved quantities. The resulting conservation laws provide deeper insights into the equation’s physical properties and invariant structures. This work advances the theoretical understanding of the LMNLSE and offers a robust framework for analyzing similar nonlinear wave equations across various physical contexts.</p>

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Lie Symmetries, Invariant Solutions, and Conservation Laws of the Logarithmic Modified Nonlinear Schrödinger Equation

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Farzaneh Alizadeh

摘要

The logarithmic modified nonlinear Schrödinger equation (LMNLSE) extends the classical nonlinear Schrödinger equation by incorporating a logarithmic nonlinearity to account for specific quantum effects and wave phenomena. This study examines the symmetry structure of the LMNLSE using the Lie symmetry (LS) method. By systematically identifying the LSs of the equation, invariant solutions are obtained, enhancing the understanding of its underlying dynamics. Furthermore, the conservation laws associated with the LMNLSE are explored through the application of Ibragimov’s theorem, utilizing symmetries to obtain conserved quantities. The resulting conservation laws provide deeper insights into the equation’s physical properties and invariant structures. This work advances the theoretical understanding of the LMNLSE and offers a robust framework for analyzing similar nonlinear wave equations across various physical contexts.