Long-Time Asymptotics of a Three-Component Coupled mKdV System
Abstract
:1. Introduction
2. An Integrable Three-Component Coupled mKdV Hierarchy
2.1. Zero Curvature Formulation
2.2. Three-Component mKdV Hierarchy
3. An Associated Oscillatory Riemann-Hilbert Problem
3.1. An Equivalent Matrix Spectral Problem
3.2. An Oscillatory Riemann-Hilbert Problem
4. Long-Time Asymptotic Behavior
4.1. Transformation of the RH Problem
4.2. Decomposition of the Spectral Induced Function
4.3. Deformation of the RH Problem
4.4. Contour Truncation
4.5. Disconnecting Contour Components
4.6. Rescaling and Reduction of the Disconnected RH Problem
4.7. The Model RH Problem and Its Solution
5. Concluding Remarks
Funding
Acknowledgments
Conflicts of Interest
References
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Ma, W.-X. Long-Time Asymptotics of a Three-Component Coupled mKdV System. Mathematics 2019, 7, 573. https://doi.org/10.3390/math7070573
Ma W-X. Long-Time Asymptotics of a Three-Component Coupled mKdV System. Mathematics. 2019; 7(7):573. https://doi.org/10.3390/math7070573
Chicago/Turabian StyleMa, Wen-Xiu. 2019. "Long-Time Asymptotics of a Three-Component Coupled mKdV System" Mathematics 7, no. 7: 573. https://doi.org/10.3390/math7070573