Dissipative solitons that cannot be trapped

Area of Science:

• Nonlinear Optics
• Quantum Mechanics
• Soliton Physics

Background:

• Dissipative solitons are self-organized structures in nonlinear systems with energy dissipation.
• High-order nonlinear dissipation introduces complex dynamics not seen in lower-order systems.
• Trapping potentials can confine or destabilize these solitons.

Purpose of the Study:

• To investigate the stability of dissipative solitons in systems with high-order nonlinear dissipation under various trapping potentials.
• To determine the conditions under which these solitons can survive or be destroyed.

Main Methods:

• Theoretical analysis of dissipative soliton dynamics.
• Numerical simulations of soliton behavior in the presence of different potential types (rigid wall, asymptotically increasing, weak).

Main Results:

• Dissipative solitons are unstable and cannot survive in the presence of rigid wall or asymptotically increasing trapping potentials.
• Solitons can persist under weak potentials, but their energies fall outside the typical range for linear quantum mechanical stationary states.

Conclusions:

• The stability of dissipative solitons is highly sensitive to the nature of nonlinear dissipation and external potentials.
• The survival of solitons in weak potentials with non-classical energies highlights unique phenomena in nonlinear dissipative systems.