THE $ \bar{\partial} $-DRESSING METHOD FOR THE TWO-DIMENSIONAL HARRY DYM EQUATION

Linlin Gui; Yufeng Zhang; Siqi Han

doi:10.11948/20250033

2025 Volume 15 Issue 6

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Linlin Gui, Yufeng Zhang, Siqi Han. THE $ \bar{\partial} $-DRESSING METHOD FOR THE TWO-DIMENSIONAL HARRY DYM EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3465-3479. doi: 10.11948/20250033

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Linlin Gui, Yufeng Zhang, Siqi Han. THE $ \bar{\partial} $-DRESSING METHOD FOR THE TWO-DIMENSIONAL HARRY DYM EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3465-3479. doi: 10.11948/20250033

THE $ \bar{\partial} $-DRESSING METHOD FOR THE TWO-DIMENSIONAL HARRY DYM EQUATION

1.
School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Author Bio: Email: mathzhang@126.com(Y. Zhang); Email: hsq2023cumt0511@126.com(S. Han)
Corresponding author: Email: guilinlin9806@163.com(L. Gui)

Abstract

Abstract

The (2+1)-dimensional Harry Dym (HD) equation is solved via the $ \bar{\partial} $-dressing method in this paper. By introducing long derivatives $ E_x $, $ E_y $ and $ E_t $ and new expressions for the kernel functions $ K $ of $ \bar{\partial} $-problem, a type of general solution of the HD equation is obtained. Under the reality of the solution $ u $ of the HD equation, several classes of exact explicit solutions of the HD equation, including the solutions with functional parameters, line solitons and rational solutions, are constructed by the $ \bar{\partial} $-dressing method.
- HD equation /
- $ \bar{\partial} $-dressing method /
- line soliton /
- rational solution
MSC: 35C08, 45Q05

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References

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