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Volume 12, Issue 3
Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System

Han-Yu Wei, En-Gui Fan & Wen-Xiu Ma

DOI: 10.4208/eajam.200121.190921

East Asian J. Appl. Math., 12 (2022), pp. 521-534.

Published online: 2022-04

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  • Abstract

Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its application, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.

  • Keywords

Integrable coupling, Guo-hierarchy, bi-Hamiltonian structure, self-consistent source.

  • AMS Subject Headings

35Q51, 35Q53, 37K40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-521, author = {Han-Yu Wei, En-Gui Fan and Wen-Xiu Ma}, title = {Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {521--534}, abstract = {

Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its application, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200121.190921}, url = {http://global-sci.org/intro/article_detail/eajam/20404.html} }
TY - JOUR T1 - Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System AU - Han-Yu Wei, En-Gui Fan & Wen-Xiu Ma JO - East Asian Journal on Applied Mathematics VL - 3 SP - 521 EP - 534 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.200121.190921 UR - https://global-sci.org/intro/article_detail/eajam/20404.html KW - Integrable coupling, Guo-hierarchy, bi-Hamiltonian structure, self-consistent source. AB -

Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its application, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.

Han-Yu Wei, En-Gui Fan and Wen-Xiu Ma. (2022). Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System. East Asian Journal on Applied Mathematics. 12 (3). 521-534. doi:10.4208/eajam.200121.190921
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