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    Area of Science:

    • Nonlinear optics
    • Computational physics
    • Mathematical modeling

    Background:

    • Nonlinear media support self-trapped beams, crucial for optical communications.
    • Traditional variational methods face challenges with analytical integration and differentiation.
    • Predicting stable beam propagation in nonlinear systems is complex.

    Purpose of the Study:

    • Introduce a numerical variational method using Rayleigh-Ritz optimization.
    • Overcome limitations of traditional analytical variational approximations.
    • Predict two-dimensional self-trapped beams in nonlinear media.

    Main Methods:

    • Numerical variational method.
    • Rayleigh-Ritz optimization principle.
    • Solving a generalized nonlinear Schrödinger equation.

    Main Results:

    • Obtained approximate soliton solutions for self-trapped beams.
    • Demonstrated the robustness of fundamental, vortex, multipole, and azimuthon beams.
    • Validated the method's accuracy in predicting beam propagation.

    Conclusions:

    • The numerical variational method effectively predicts self-trapped beams.
    • The technique is versatile for various beam types and nonlinear models.
    • Offers potential for designing sophisticated soliton profiles.