Abstract
AbstractThis paper concerns the initial value problem of a coupled complex mKdV (CCMKDV) equations $$ \begin{aligned} &u_{t}+u_{xxx}+6 \bigl( \vert u \vert ^{2}+ \vert v \vert ^{2} \bigr)u_{x}+6u\bigl( \vert v \vert ^{2} \bigr)_{x}=0, \\ &v_{t}+v_{xxx}+6\bigl( \vert u \vert ^{2}+ \vert v \vert ^{2}\bigr)v_{x}+6v \bigl( \vert u \vert ^{2}\bigr)_{x}=0, \end{aligned} $$
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proposed by Yang (Nonlinear Waves in Integrable and Nonintegrable Systems, 2010), which is associated with a $4 \times 4$
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scattering problem. Based on matrix spectral analysis, a fourth-order matrix Riemann–Hilbert problem is formulated. By solving a specific nonregular Riemann–Hilbert problem with zeros, we present the N-soliton solutions for the CCMKDV system. Moreover, the single-soliton solutions are displayed graphically.
Funder
Foundation of Henan Educational Committee
High-level talent program of Henan University of Technology
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference39 articles.
1. Yang, J.K.: Nonlinear Waves in Integrable and Nonintegrable Systems. SIAM, Philadelphia (2010)
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3. Ablowitz, M.J., Kaup, D.J., Newell, A.C.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249 (1974)
4. Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, Cambridge (2004)
5. Rogers, C., Shadwick, W.E.: Bäcklund Transformations and Their Applications. Academic Press, New York (1982)
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