| Citation: |
Guo Cheng, Peng Zhao. A RIEMANN-HILBERT METHOD TO FINITE GAP SOLUTIONS OF THE EXTENDED MODIFIED KORTEWEG-DE VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2287-2313. doi: 10.11948/20250340
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A RIEMANN-HILBERT METHOD TO FINITE GAP SOLUTIONS OF THE EXTENDED MODIFIED KORTEWEG-DE VRIES EQUATION
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Abstract
In this paper we use finite gap integration method and Riemann-Hilbert method to obtain finite gap solutions of the extended modified Korteweg-de Vries equation. Based on the techniques developed in long-time asymptotics, we show that the Baker-Akhiezer function of the extended modified Korteweg-de Vries equation can be described by solvable matrix Riemann-Hilbert problems with $ \sigma_2 $- symmetry condition on $ \mathbb {C} $. The procedure avoids solving Dubrovin's equations and Jacobi inverse problem.
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References
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Guo Cheng, Peng Zhao. A RIEMANN-HILBERT METHOD TO FINITE GAP SOLUTIONS OF THE EXTENDED MODIFIED KORTEWEG-DE VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2287-2313. doi: 10.11948/20250340
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Figure 1.
The oriented contour in the
$ k $ -
Figure 2.
The oriented contour in the
$ k $ -
Figure 3.
Case A; cuts on real axis for defocusing emKdV.
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Figure 4.
Case A; vertical cuts for focusing emKdV.
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Figure 5.
Case B; cut on real axis for defocusing emKdV.
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Figure 6.
Case B; vertical cuts for focusing emKdV.