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The random noise modulations on the nonlinear Chiral Schrödinger structures
Hadil Alhazmi1, Sanaa A Bajri1, E K El-Shewy2,3
1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Researchers explored the Chiral nonlinear Schrödinger equation (CNLSE) with time-varying noise, finding new stochastic solutions relevant to quantum physics and Hall effects. Noise significantly influences wave propagation and solution behavior.
Area of Science:
- Quantum Physics
- Nonlinear Dynamics
- Mathematical Physics
Background:
- The Chiral nonlinear Schrödinger equation (CNLSE) models edge states in quantum Hall effect phenomena.
- Understanding stochastic behavior in nonlinear systems is crucial for advanced physics applications.
Purpose of the Study:
- To derive novel stochastic solutions for the CNLSE with time-dependent multiplicative noise.
- To analyze the influence of noise and model parameters on the behavior of CNLSE solutions.
Main Methods:
- Application of the sine-Gordon expansion method.
- Analysis of solitary and dissipative structures (rational, envelope, shock).
- Numerical simulations to illustrate deterministic and stochastic solution dynamics.
Main Results:
- New stochastic solutions for the CNLSE were successfully obtained.
- Identified that multiplicative noise significantly impacts envelope growth, damping, and wave propagation.
- Demonstrated the formation of rational, envelope, and shock-type solutions.
Conclusions:
- The study provides crucial insights into the role of noise in quantum physics phenomena modeled by the CNLSE.
- The developed methodology offers potential for solving more complex problems in applied sciences.
- The findings contribute to the understanding of wave propagation and stability in stochastic nonlinear systems.
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