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<p>This paper examines the generalized Fokas–Lenells equation, which describes ultrashort pulse propagation in nonlinear optical media, incorporating higher-order dispersion, self-steepening, and intermodal effects. We apply the multiplier method to derive two independent conservation laws, which provide expressions for conserved densities and fluxes. By directly substituting a traveling wave ansatz into these densities, we obtain two first integrals, which are combined into a single equation governing the wave profile amplitude. Exact solutions are obtained for two regimes: for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12596_2025_2898_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=1\)</EquationSource> </InlineEquation>, we derive periodic waves expressed in terms of Jacobi elliptic functions, along with their degenerate solitary wave limits, and for arbitrary integer <i>n</i>, we obtain closed form solitary wave profiles under a set of natural parameter constraints using an exponential ansatz. Finally, we compute the conserved quantities associated with each solitary wave solution, expressing them in terms of previously computed definite integrals. The exact solutions and their corresponding conserved quantities serve as reliable benchmarks for validating numerical simulations and offer insights for guiding experimental studies in nonlinear optics.</p>

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Conservation laws and exact solutions of the generalized Fokas–Lenells equation

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Daniil R. Nifontov,
  • Nikolay A. Kudryashov,
  • Sofia F. Lavrova

摘要

This paper examines the generalized Fokas–Lenells equation, which describes ultrashort pulse propagation in nonlinear optical media, incorporating higher-order dispersion, self-steepening, and intermodal effects. We apply the multiplier method to derive two independent conservation laws, which provide expressions for conserved densities and fluxes. By directly substituting a traveling wave ansatz into these densities, we obtain two first integrals, which are combined into a single equation governing the wave profile amplitude. Exact solutions are obtained for two regimes: for \(n=1\) , we derive periodic waves expressed in terms of Jacobi elliptic functions, along with their degenerate solitary wave limits, and for arbitrary integer n, we obtain closed form solitary wave profiles under a set of natural parameter constraints using an exponential ansatz. Finally, we compute the conserved quantities associated with each solitary wave solution, expressing them in terms of previously computed definite integrals. The exact solutions and their corresponding conserved quantities serve as reliable benchmarks for validating numerical simulations and offer insights for guiding experimental studies in nonlinear optics.