Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Conservation laws by symmetries and adjoint symmetries
Pages: 707 - 721, Issue 4, August 2018

doi:10.3934/dcdss.2018044      Abstract        References        Full text (399.5K)           Related Articles

Wen-Xiu Ma - Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States (email)

1 S. C. Anco and G. Bluman, Direct computation of conservation laws from filed equations, Phys. Rev. Lett., 78 (1997), 2869-2873.       
2 S. C. Anco and G. Bluman, Derivation of conservation laws from nonlocal symmetries of differential equations, J. Math. Phys., 37 (1996), 2361-2375.       
3 G. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York-Berlin, 1989.       
4 B. Fuchsstiener, Application of hereditary symmetries to nonlinear evolution equations, Nonlinear Anal., 3 (1979), 849-862.       
5 B. Fuchsstiener and A. C. Fokas, Symplectic structures, their B├Ącklund transformations and hereditary symmetries, Physica D, 4 (1981), 47-66.       
6 B. Fuchssteiner and W. X. Ma, An approach to master symmetries of lattice equations, in: Symmetries and Integrability of Difference Equations (Canterbury, 1996) (ed. P. A. Clarkson and F. W. Nijhoff), London Math. Soc. Lecture Note Ser., 255, Cambridge Univ. Press, Cambridge, 1999, 247-260.       
7 N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, Holland, 1985.       
8 N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., 333 (2007), 311-328.       
9 N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math. Theor., 44 (2011), 432002 (8pp).
10 X. Y. Li and Q. L. Zhao, A new integrable symplectic map by the binary nonlinearization to the super AKNS system, J. Geom. Phys., 121 (2017), 123-137.       
11 X. Y. Li, Q. L. Zhao, Y. X. Li and H. H. Dong, Binary Bargmann symmetry constraint associated with $3\times 3$ discrete matrix spectral problem, J. Nonlinear Sci. Appl., 8 (2015), 496-506.       
12 Y. S. Li, Some algebraic properties of "$C$-integrable" nonlinear equations I. Burgers equation and Calogero equation, Sci. China Ser. A, 33 (1990), 513-520.       
13 W. X. Ma and B. Fuchssteiner, Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations, J. Math. Phys., 40 (1999), 2400-2418.       
14 W. X. Ma, $K$-symmetries and $\tau$-symmetries of evolution equations and their Lie algebras, J. Phys. A: Math. Gen., 23 (1990), 2707-2716.       
15 W. X. Ma, New finite-dimensional integrable systems by symmetry constraint of the KdV equations, J. Phys. Soc. Jpn., 64 (1995), 1085-1091.       
16 W. X. Ma and W. Strampp, An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems, Phys. Lett. A, 185 (1994), 277-286.       
17 W. X. Ma, The algebraic structures of isospectral Lax operators and applications to integrable equations, J. Phys. A: Math. Gen., 25 (1992), 5329-5343.       
18 W. X. Ma, Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations, J. Math. Phys., 33 (1992), 2464-2476.       
19 W. X. Ma, A method of zero curvature representation for constructing symmetry algebras of integrable systems, in: Proceedings of the 21st International Conference on the Differential Geometry Methods in Theoretical Physics (ed. M. L. Ge), World Scientific, Singapore, 1993, 535-538.
20 W. X. Ma, Conservation laws of discrete evolution equations by symmetries and adjoint symmetries, Symmetry, 7 (2015), 714-725.       
21 W. X. Ma and R. G. Zhou, Adjoint symmetry constraints leading to binary nonlinearization, J. Nonlinear Math. Phys., 9 (2002), 106-126.       
22 P. Morando and S. Pasquero, The symmetry in the structure of dynamical and adjoint symmetries of second-order differential equations, J. Phys. A: Math. Gen., 28 (1995), 1943-1955.       
23 C. S. Morawetz, Variations on conservation laws for the wave equation, Bull. Amer. Math. Soc. (N.S.), 37 (2000), 141-154.       
24 P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics 107, Springer-Verlag, New York-Berlin, 1986.       
25 P. J. Olver, Evolution equations possessing infinitely many symmetries, J. Math. Phys., 18 (1977), 1212-1215.       
26 W. Sarlet and A. Ramos, Adjoint symmetries, separability, and volume forms, J. Math. Phys., 41 (2000), 2877-2888.       
27 C. Tian, New strong symmetry, symmetries and Lie algebra of Burgers' equation, Sci. Sinica Ser. A, 31 (1988), 141-151.       
28 G. Z. Tu and M. Z. Qin, The invariant groups and conservation laws of nonlinear evolution equations-an approach of symmetric function, Sci. Sinica, 24 (1981), 13-26.       
29 X. R. Wang, X. E. Zhang and P. Y. Zhao, Binary nonlinearization for AKNS-KN coupling system, Abstr. Appl. Anal., 2014 (2014), Art. ID 253102, 12 pp.       

Go to top