Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval
By Shou‐Fu Tian. 2018
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In this paper, we study the initial-boundary value problems of the coupled modified Korteweg-de Vries equation formulated on the finite interval with Lax pairs involving \begin{document}$3× 3$\end{document} matrices via the Fokas method. We write the solution in terms of the solution of a \begin{document}$3× 3$\end{document} Riemann-Hilbert problem. The relevant jump matrices are explicitly expressed in terms of the three matrix-value spectral functions \begin{document}$s(k)$\end{document} , \begin{document}$S(k)$\end{document} , and \begin{document}$S_{L}(k)$\end{document} , which are determined by the initial values, boundary values at \begin{document}$x = 0$\end{document} , and at \begin{document}$x = L$\end{document} , respectively. Some of the boundary values are known for a well-posed problem, however, the remaining boundary data are unknown. By using the so-called global relation, the unknown boundary values can be expressed in terms of the given initial and boundary data via a Gelfand-Levitan-Marchenko representation.
Subfields: Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5540cae221dd840f499e77971500268622ae5ceb
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In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity (2019, background): “In Figure 1(a), dark soliton solution for Equation (15) and (b) bright soliton solution for Equation (16), with these parameters values β1 = 2,β2 = 4,β3 = 2, = 8, η = 2, ζ0 = 0.”