Self-Consistent Sources and Conservation Laws for Super Tu Equation Hierarchy


Based upon the basis of Lie super algebra B(0,1), the super Tu equation hierarchy with self-con- sistent sources was presented. Furthermore, the infinite conservation laws of above hierarchy were given.

Share and Cite:

Tao, S. (2015) Self-Consistent Sources and Conservation Laws for Super Tu Equation Hierarchy. Journal of Applied Mathematics and Physics, 3, 428-435. doi: 10.4236/jamp.2015.34054.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Ma, W.X. and Strampp, W. (1994) An Explicit Symmetry Constraint for the Lax Pairs of AKNS Systems. Physics Letters A, 185, 277-286.
[2] Ma, W.X. (2003) Soliton, Positon and Negaton Solutions to a Schrödinger Self-Consistent Source Equation. Journal of the Physical Society of Japan, 72, 3017-3019.
[3] Ma, W.X. and Geng, X.G. (2001) B?cklund Transformations of Soliton Systems from Symmetry Constraints. CRM Proceedings and Lecture Notes, 29, 313-323.
[4] Hu, X.B. (1997) An Approach to Generate Superextensions of Integrable Systems. Journal of Physics A: Mathematical and General, 30, 619-632.
[5] Ma, W.X., He, J.S. and Qin, Z.Y. (2008) A Supertrace Identity and Its Applications to Super Integrable Systems. Journal of Mathematical Physics, 49, Article ID: 033511.
[6] Wang, X.Z. and Liu, X.K. (2010) Two Types of Lie Super-Algebra for the Super-Integrable Tu-Hierarchy and Its Super- Hamiltonian Structure. Communications in Nonlinear Science and Numerical Simulation, 15, 2044-2049.
[7] Yu, J., Han, J.W. and He, J.S. (2009) Binary Nonlinearization of the Super AKNS System under an Implicit Symmetry Constraint. Journal of Physics A: Mathematical and Theoretical, 42, Article ID: 465201.
[8] Yu, J., He, J.S., Ma, W.X. and Cheng, Y. (2010) The Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Dirac System. Chinese Annals of Mathematics, Series B, 31, 361-372.
[9] Liu, Q.P. (1995) Darboux Transformations for Supersymmetric Korteweg-De Equations. Letters in Mathematical Physics, 35, 115-122.
[10] Siddiq, M., Hassan, M. and Saleem, U. (2006) On Darboux Transformation of the Supersymmetric Sine-Gordon Equation. Journal of Physics A: Mathematical and General, 39, 7313-7318.
[11] Zeng, Y.B., Ma, W.X. and Lin, R.L. (2000) Integration of the Soliton Hierarchy with Self-Consistent Sources. Journal of Mathematical Physics, 41, 5453-5489.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.