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Volume 6, Issue 2
Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data

Hongyi Zhang & Yufeng Zhang

DOI: 10.12150/jnma.2024.413

J. Nonl. Mod. Anal., 6 (2024), pp. 413-434.

Published online: 2024-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we apply $\overline{\partial}$-steepest descent method to analyze the long-time asymptotics of complex mKdV equation with the initial value belonging to weighted Sobolev spaces. Firstly, the Cauchy problem of the complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying the solution of the Riemann-Hilbert problem.

  • Keywords

Riemann-Hilbert problem, complex mKdV equation, $\overline{\partial}$-steepest descent method, long-time asymptotics.

  • AMS Subject Headings

35Q51, 35Q15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-413, author = {Zhang , Hongyi and Zhang , Yufeng}, title = {Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {2}, pages = {413--434}, abstract = {

In this paper, we apply $\overline{\partial}$-steepest descent method to analyze the long-time asymptotics of complex mKdV equation with the initial value belonging to weighted Sobolev spaces. Firstly, the Cauchy problem of the complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying the solution of the Riemann-Hilbert problem.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.413}, url = {http://global-sci.org/intro/article_detail/jnma/23183.html} }
TY - JOUR T1 - Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data AU - Zhang , Hongyi AU - Zhang , Yufeng JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 413 EP - 434 PY - 2024 DA - 2024/06 SN - 6 DO - http://doi.org/10.12150/jnma.2024.413 UR - https://global-sci.org/intro/article_detail/jnma/23183.html KW - Riemann-Hilbert problem, complex mKdV equation, $\overline{\partial}$-steepest descent method, long-time asymptotics. AB -

In this paper, we apply $\overline{\partial}$-steepest descent method to analyze the long-time asymptotics of complex mKdV equation with the initial value belonging to weighted Sobolev spaces. Firstly, the Cauchy problem of the complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying the solution of the Riemann-Hilbert problem.

Hongyi Zhang & Yufeng Zhang. (2024). Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data. Journal of Nonlinear Modeling and Analysis. 6 (2). 413-434. doi:10.12150/jnma.2024.413
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