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Updated: Jun 22, 2025
12:18
Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
17.0K
-symmetric KdV solutions and their algebraic extension with zero-width resonances
Kumar Abhinav1, Aradhya Shukla2, Prasanta K Panigrahi3,4
1Centre for Theoretical Physics and Natural Philosophy, Nakhonsawan Studiorum for Advanced Studies, Mahidol University, Nakhonsawan, 60130, Thailand. kumar.abh@mahidol.ac.th.
Scientific Reports
|July 3, 2024
Summary
Researchers identified complex breather and soliton solutions for KdV and mKdV equations using a Pöschl-Teller potential. Further extensions are needed to achieve the broken-phase, enabling non-trivial zero-width resonances.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
Background:
- The Korteweg-de Vries (KdV) and modified KdV (mKdV) equations model various nonlinear phenomena.
- Pöschl-Teller potentials are often used in quantum mechanics and nonlinear systems.
Purpose of the Study:
- To identify complex breather and soliton solutions for KdV and mKdV equations.
- To investigate the conditions for achieving the broken-phase solutions.
Main Methods:
- Utilizing a Pöschl-Teller type potential with specific symmetry properties.
- Analyzing the spectral properties of the potential in the complex plane.
Main Results:
- Complex breather and soliton solutions were identified for KdV and mKdV equations under a Pöschl-Teller potential.
- These solutions initially represented the unbroken-phase due to isospectrality with an infinite potential well.
- Achieving the broken-phase requires an extended potential satisfying the potential algebra and supporting zero-width resonances.
Conclusions:
- The study identifies a class of solutions but highlights the need for potential extension to access the broken-phase.
- The findings pave the way for exploring more complex nonlinear phenomena and resonances.
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