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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2109.02901 (nlin)
[Submitted on 7 Sep 2021]

Title:Inverse scattering transform and multiple high-order pole solutions for the nonlocal focusing and defocusing modified Korteweg-de Vries equation with the nonzero boundary conditions

Authors:Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang
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Abstract:We extend the Riemann-Hilbert (RH) method to study the inverse scattering transformation and high-order pole solutions of the focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with nonzero boundary conditions (NZBCs) at infinity and successfully find its multiple soliton solutions with one high-order pole and multiple high-order poles. By introducing the generalized residue formula, we overcome the difficulty caused by calculating the residue conditions corresponding to the higher-order poles. In accordance with the Laurent series of reflection coefficient and oscillation term, the determinant formula of the high-order pole solution with NZBCs is established. Finally, combined with specific parameters, the dynamic propagation behaviors of the high-order pole solutions are further analyzed and some very interesting phenomena are obtained, including kink solution, anti kink solution, rational solution and breathing-soliton solution.
Comments: 26 pages, 4 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Cite as: arXiv:2109.02901 [nlin.SI]
  (or arXiv:2109.02901v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2109.02901

Submission history

From: Shou-Fu Tian [view email]
[v1] Tue, 7 Sep 2021 06:57:38 UTC (502 KB)
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