Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation

المؤلفون المشاركون

Xu, Xi-Xiang
Zhang, Ning

المصدر

Mathematical Problems in Engineering

العدد

المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-15، 15ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2020-12-30

دولة النشر

مصر

عدد الصفحات

15

التخصصات الرئيسية

هندسة مدنية

الملخص EN

Two integrable hierarchies are derived from a novel discrete matrix spectral problem by discrete zero curvature equations.

They correspond, respectively, to positive power and negative power expansions of Lax operators with respect to the spectral parameter.

The bi-Hamiltonian structures of obtained hierarchies are established by a pair of Hamiltonian operators through discrete trace identity.

The Liouville integrability of the obtained hierarchies is proved.

Through a gauge transformation of the Lax pair, a Darboux–Bäcklund transformation is constructed for the first nonlinear different-difference equation in the negative hierarchy.

Ultimately, applying the obtained Darboux–Bäcklund transformation, two exact solutions are given by means of mathematical software.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

Zhang, Ning& Xu, Xi-Xiang. 2020. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195890

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

Zhang, Ning& Xu, Xi-Xiang. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1195890

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

Zhang, Ning& Xu, Xi-Xiang. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195890

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-1195890