Riemann-Hilbert Problems of a Six-Component mKdV System and its Soliton Solutions
Based on a 4 × 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.
Key wordsintegrable hierarchy Riemann-Hilbert problem soliton solution
2010 MR Subject Classification35Q53 37K10 37K20
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The author would also like to thank Batwa S, Gu X, Ju L, Lafortune S, Malisoff M, Manukure S, McAnally M, Tian J, Wang F D, Yong Y L, Zhang H Q, and Zhou Y for their valuable discussions.
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