A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations

Yongtang Wu; Xianguo Geng; Xingbiao Hu; Siming Zhu

doi:10.1016/S0375-9601(99)00163-2

A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations

Yongtang Wu^*
, Xianguo Geng
, Xingbiao Hu
, Siming Zhu

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

172 Citations (Scopus)

Abstract

By introducing a 4 X 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.

Original language	English
Pages (from-to)	259-264
Number of pages	6
Journal	Physics Letters A
Volume	255
Issue number	4-6
DOIs	https://doi.org/10.1016/S0375-9601(99)00163-2
Publication status	Published - 17 May 1999
Externally published	Yes

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10.1016/S0375-9601(99)00163-2

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title = "A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations",

abstract = "By introducing a 4 X 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.",

author = "Yongtang Wu and Xianguo Geng and Xingbiao Hu and Siming Zhu",

note = "Funding Information: This work was partially supported by Hong Kong RGC/97-98/21, Chinese Academy of Sciences and Henan Science Foundation. Project 19671074 was supported by National Natural Science Foundation of China.",

year = "1999",

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T1 - A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations

AU - Wu, Yongtang

AU - Geng, Xianguo

AU - Hu, Xingbiao

AU - Zhu, Siming

N1 - Funding Information: This work was partially supported by Hong Kong RGC/97-98/21, Chinese Academy of Sciences and Henan Science Foundation. Project 19671074 was supported by National Natural Science Foundation of China.

PY - 1999/5/17

Y1 - 1999/5/17

N2 - By introducing a 4 X 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.

AB - By introducing a 4 X 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.

UR - https://www.scopus.com/pages/publications/0345985752

U2 - 10.1016/S0375-9601(99)00163-2

DO - 10.1016/S0375-9601(99)00163-2

M3 - Journal article

AN - SCOPUS:0345985752

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VL - 255

SP - 259

EP - 264

JO - Physics Letters A

JF - Physics Letters A

IS - 4-6

ER -

A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations

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