Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses

Area of Science:

• Nonlinear physics
• Optical fiber communications
• Wave propagation

Background:

• The nonlinear Schrödinger equation models phenomena like optical fiber signal transmission.
• Shock waves (SWs) are crucial in energy domain conversion.
• Previous studies focused on continuum models, leaving discrete systems less explored.

Purpose of the Study:

• Investigate shock wave (SW) propagation in a discrete nonlinear Schrödinger equation with viscosity.
• Analyze the stability and velocity dependence of SWs in discrete systems.
• Compare discrete model behavior to its continuum counterpart.

Main Methods:

• Utilized a discrete version of the normal-dispersion nonlinear Schrödinger equation.
• Incorporated viscosity to model weakly lossy media, relevant to optical fiber arrays.
• Analyzed shock wave stability, velocity, and width dependence on system parameters.

Main Results:

• Confirmed stability of shock waves in the discrete model, consistent with continuum models.
• Observed a linear relationship between SW velocity and background amplitude in strongly discrete cases.
• Found SW velocity vanishes with viscosity in the underdamped case, a potentially universal feature.

Conclusions:

• The discrete nonlinear Schrödinger equation supports stable shock wave propagation.
• Discrete systems exhibit unique velocity-amplitude relationships compared to continuum models.
• The vanishing velocity with viscosity suggests universal behavior in finite discrete and continuum systems.