Well-posedness for a coupled system of gKdV equations in analytic spaces

Malika Amir; Aissa Boukarou; Safa M. Mirgani; M'hamed Kesri; Khaled Zennir; Mdi Begum Jeelani; Malika Amir; Aissa Boukarou; Safa M. Mirgani; M'hamed Kesri; Khaled Zennir; Mdi Begum Jeelani

doi:10.3934/era.2025184

Electronic Research Archive

2025, Volume 33, Issue 7: 4119-4134. doi: 10.3934/era.2025184

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Research article

Well-posedness for a coupled system of gKdV equations in analytic spaces

1.
University of Science and Technology Houari Boumediene, Bab Ezzouar, Algeria
2.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
3.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 12 April 2025 Revised: 17 June 2025 Accepted: 25 June 2025 Published: 04 July 2025

In this article, a Cauchy problem for a coupled system of the generalized Korteweg-de Vries equations (gKdV) is considered. In the periodic case, it is shown that the system is locally well-posed in a large class of analytic functions and conditions for which weak solutions extend holomorphically in a symmetric strip of the complex plane around the $ x $-axis at large times. In addition, the uniform analyticity radius of the solution does not change as time progresses. Also, information about the regularity of the solution in the time variable is obtained.
- nonlinear equations,
- gKdV system,
- local well-posedness,
- energy and industry,
- analytic spaces
Citation: Malika Amir, Aissa Boukarou, Safa M. Mirgani, M'hamed Kesri, Khaled Zennir, Mdi Begum Jeelani. Well-posedness for a coupled system of gKdV equations in analytic spaces[J]. Electronic Research Archive, 2025, 33(7): 4119-4134. doi: 10.3934/era.2025184

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Abstract

In this article, a Cauchy problem for a coupled system of the generalized Korteweg-de Vries equations (gKdV) is considered. In the periodic case, it is shown that the system is locally well-posed in a large class of analytic functions and conditions for which weak solutions extend holomorphically in a symmetric strip of the complex plane around the $ x $-axis at large times. In addition, the uniform analyticity radius of the solution does not change as time progresses. Also, information about the regularity of the solution in the time variable is obtained.

References

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