Wide localized solitons in systems with time- and space-modulated nonlinearities

Area of Science:

• Nonlinear dynamics
• Mathematical physics
• Quantum mechanics

Background:

• Nonautonomous nonlinear Schrödinger equations (NLSEs) present significant challenges in theoretical physics.
• Existing methods often rely on specific ansatz assumptions for the wave function.
• Generalizing solutions for time- and space-dependent nonlinearities and potentials is crucial.

Purpose of the Study:

• To develop a novel method for solving classes of nonautonomous, nonlinear Schrödinger equations.
• To find wide localized (in space) soliton solutions.
• To generalize existing solution procedures and extend the scope of solvable NLSEs.

Main Methods:

• Application of point canonical transformations.
• Transformation of nonautonomous NLSEs into explicitly solvable forms.
• Generalization of cubic and quintic nonlinearities and external potentials.

Main Results:

• Explicit solutions for specific classes of nonautonomous, nonlinear Schrödinger equations.
• Identification of wide localized soliton solutions.
• Demonstration of the method's ability to handle time- and space-dependent nonlinearities and potentials.

Conclusions:

• Point canonical transformations offer a powerful tool for solving complex NLSEs.
• The developed method provides a generalized approach to finding soliton solutions.
• This work expands the analytical tractability of nonlinear wave phenomena.