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arXiv · 2110.08763

Spectral analysis and long-time asymptotics of complex mKdV equation

Hong-Yi Zhang·Yu-Feng Zhang
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Abstract

In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem of complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering matrix. After that Riemann-Hilbert problems are converted through a decomposition of the matrix-valued spectral function and factorizations of the jump matrix for Riemann-Hilbert problem. Finally, by solving the last model problem, the long-time asymptotics of complex mKdV equation are derived.

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BibTeXRIS

Hong-Yi Zhang, Yu-Feng Zhang. 2021-10-17. Spectral analysis and long-time asymptotics of complex mKdV equation. https://doi.org/10.1063/5.0073909

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