Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach

Adil Jhangeer

doi:10.33187/jmsm.411423

EN

Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach

Abstract

In this paper, non-variational bi-Hamiltonian system of shallow-water waves propagation is considered. Lie point generators are calculated and one dimensional optimal system of its subalgebras up to conjugacy classes are reported. Then similarity variables are computed by using these conjugacy classes which are further utilized for the reduction of considered system. Then, a transformation is used to convert the system from non-variational to variational system, thus standard Lagrangian is computed. Noether operators are calculated by using Noether approach and local conserved quantity is discussed for the new fourth order system of partial differential equations (PDEs). Further, inverse transformation is applied to get the corresponding local conserved quantity for the considered non-variational problem. Moreover, this local conservation law with the help of double reduction theorem is utilized to reduce the system.

Keywords

Lagrangian,Noether operator,Conserved quantities

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Adil Jhangeer ^*
Saudi Arabia

Publication Date

May 27, 2018

Submission Date

March 31, 2018

Acceptance Date

May 22, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

DOI

https://doi.org/10.33187/jmsm.411423

IZ

https://izlik.org/JA99TD47CU

APA

Jhangeer, A. (2018). Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach. Journal of Mathematical Sciences and Modelling, 1(1), 39-44. https://doi.org/10.33187/jmsm.411423

AMA

1.Jhangeer A. Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach. Journal of Mathematical Sciences and Modelling. 2018;1(1):39-44. doi:10.33187/jmsm.411423

Chicago

Jhangeer, Adil. 2018. “Reduction of Non-Variational Bi-Hamiltonian System of Shallow-Water Waves Propagation via Symmetry Approach”. Journal of Mathematical Sciences and Modelling 1 (1): 39-44. https://doi.org/10.33187/jmsm.411423.

EndNote

Jhangeer A (May 1, 2018) Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach. Journal of Mathematical Sciences and Modelling 1 1 39–44.

IEEE

[1]A. Jhangeer, “Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 1, pp. 39–44, May 2018, doi: 10.33187/jmsm.411423.

ISNAD

Jhangeer, Adil. “Reduction of Non-Variational Bi-Hamiltonian System of Shallow-Water Waves Propagation via Symmetry Approach”. Journal of Mathematical Sciences and Modelling 1/1 (May 1, 2018): 39-44. https://doi.org/10.33187/jmsm.411423.

JAMA

1.Jhangeer A. Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach. Journal of Mathematical Sciences and Modelling. 2018;1:39–44.

MLA

Jhangeer, Adil. “Reduction of Non-Variational Bi-Hamiltonian System of Shallow-Water Waves Propagation via Symmetry Approach”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 1, May 2018, pp. 39-44, doi:10.33187/jmsm.411423.

Vancouver

1.Adil Jhangeer. Reduction of non-variational bi-Hamiltonian system of shallow-water waves propagation via symmetry approach. Journal of Mathematical Sciences and Modelling. 2018 May 1;1(1):39-44. doi:10.33187/jmsm.411423

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