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A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations

✍ Scribed by Yongtang Wu; Xianguo Geng; Xingbiao Hu; Siming Zhu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
68 KB
Volume
255
Category
Article
ISSN
0375-9601

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✦ Synopsis

By introducing a 4 = 4 matrix spectral problem with three potentials, we propose a new hierarchy of nonlinear evolution equations. A typical equation in the hierarchy is a generalization of the Hirota-Satsuma coupled Korteweg-de Vries equation. Also, it is shown that the hierarchy possesses the generalized Hamiltonian form. Further, a Miura transformation related to the typical equation and its reductions are derived, from which some new coupled modified Korteweg-de Vries equations are obtained.

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Prolongation structures of a generalized
Prolongation structures of a generalized coupled Korteweg-de Vries equation and Miura transformation
✍ Yuan-Hao Cao; Deng-Shan Wang 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 187 KB

In this paper, the prolongation structures of a generalized coupled Korteweg-de Vries (KdV) equation are investigated and two integrable coupled KdV equations associated with their Lax pairs are derived. Furthermore, a Miura transformation related to a integrable coupled KdV equation is derived, fro