Wide vector solitons in systems with time- and space-modulated nonlinearities.

Area of Science:

• Nonlinear Physics
• Quantum Optics
• Mathematical Physics

Background:

• Nonautonomous nonlinear Schrödinger equations model complex physical phenomena.
• Solving these equations is challenging due to time- and space-dependent nonlinearities.
• Vector soliton solutions are crucial for understanding wave propagation and quantum systems.

Purpose of the Study:

• To develop a method for solving specific classes of two coupled nonautonomous nonlinear Schrödinger equations.
• To identify wide localized vector soliton solutions.
• To explore the applicability of these solutions in Bose-condensed atoms and optical fibers.

Main Methods:

• Application of point canonical transformations.
• Solving equations with cubic and quintic time- and space-dependent nonlinearities.
• Derivation of vector soliton solutions.

Main Results:

• A class of wide localized vector soliton solutions for nonautonomous nonlinear Schrödinger equations was found.
• The method successfully handles specific cubic and quintic nonlinearities.
• The solutions are applicable to diverse physical systems.

Conclusions:

• Point canonical transformations provide an effective tool for solving challenging nonlinear equations.
• The discovered vector solitons offer insights into Bose-condensed atoms and ultrashort pulse propagation.
• This work advances the theoretical understanding of nonlinear wave phenomena.