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Soliton management in a variable-coefficient coupled dispersionless system via Darboux transformation
H W A Riaz1,2, Y Yildirim3,4, Altaf Alshuhail5
1School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan, PR China.
Scientific Reports
|April 21, 2026
Summary
This study explores an integrable dispersionless system with time-varying coupling. Researchers found that modulation controls soliton behavior, enabling management of their trajectories and properties.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Integrable Systems
Background:
- Dispersionless systems are fundamental in physics.
- Integrable systems offer exact solutions for complex phenomena.
- Time-dependent coefficients introduce challenges in analyzing system dynamics.
Purpose of the Study:
- To investigate the integrability of a coupled dispersionless system with a time-dependent nonlinear coupling.
- To construct multi-soliton solutions and traveling wave solutions.
- To analyze the effect of temporal modulation on soliton dynamics.
Main Methods:
- Construction of a Zakharov-Shabat type Lax pair.
- Application of Darboux transformations for Wronskian-type solutions.
- Time reparametrization to an autonomous form.
Main Results:
- The system is shown to be integrable despite temporal dependence.
- Explicit families of bright and dark traveling waves are derived.
- Modulation function reshapes soliton trajectories and properties.
Conclusions:
- The temporal modulation does not alter the intrinsic traveling-wave dynamics.
- The modulation allows for controlled management of soliton amplitudes, velocities, and trajectories.
- This framework provides a method for engineering soliton behavior in nonlinear systems.
Keywords:
Coupled dispersionless systemDarboux transformationSoliton managementVariable-coefficient systemWronskian solutions.More Related Videos
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