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A hierarchy of non-isospectral multi-component AKNS equations and its integrable couplings. (English) Zbl 1209.37081
Summary: A hierarchy of non-isospectral multi-component AKNS equations is derived from an arbitrary order matrix spectral problem. As a reduction, non-isospectral multi-component Schrödinger equations are obtained. Moreover, new non-isospectral integrable couplings of the resulting AKNS soliton hierarchy are constructed by enlarging the associated matrix spectral problem.

37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q55NLS-like (nonlinear Schrödinger) equations
35Q51Soliton-like equations
Full Text: DOI
[1] Ablowitz, M. J.; Clarkson, P. A.: Soliton, nonlinear evolution equation and inverse scattering. (1991) · Zbl 0762.35001
[2] Wadati, M.: Knot theory and integrable systems. Important developments in soliton theory. Springer series in nonlinear dynamics, 468-486 (1993) · Zbl 0813.35101
[3] Dickey, L. A.: Soliton equations and Hamiltonian systems. (2003) · Zbl 1140.35012
[4] Chen, D. Y.: Soliton introduction. (2006)
[5] Hikami, K.; Wadati, M.: J. math. Phys.. 44, 3569 (2003)
[6] Tu, G. Z.: J. math. Phys.. 30, 330 (1989)
[7] Hu, X. B.: J. phys. A: math. Gen.. 27, 2497 (1994)
[8] Hu, X. B.; Tam, H. W.: Inverse problems. 17, 319 (2001)
[9] Ma, W. X.; Xu, X. X.: Int. J. Theor. phys.. 43, 219 (2004)
[10] Xu, X. X.: Phys. lett. A. 301, 250 (2002)
[11] Zhang, D. J.; Chen, D. Y.: J. phys. A. 35, 7225 (2002)
[12] Sun, Y. P.; Chen, D. Y.; Xu, X. X.: Phys. lett. A. 359, 47 (2006)
[13] Sun, Y. P.; Chen, D. Y.; Xu, X. X.: Nonlinear anal.. 64, 2604 (2006)
[14] Sun, Y. P.; Chen, D. Y.: Chaos solitons fractals. 29, 978 (2006)
[15] Tsuchida, T.; Wadati, M.: J. phys. Soc. jpn.. 67, 1175 (1998)
[16] Tsuchida, T.; Wadati, M.: Phys. lett. A. 257, 53 (1999)
[17] Ma, W. X.: Phys. lett. A. 367, 473 (2007)
[18] Guo, F. G.; Zhang, Y. F.: J. math. Phys.. 44, 5793 (2003)
[19] Zhang, Y. F.: Phys. lett. A. 342, 82 (2005)
[20] Tam, H. W.; Zhang, Y. F.: Chaos solitons fractals. 23, 963 (2005)
[21] Ma, W. X.; Fuchssteiner, B.: Chaos solitons fractals. 7, 1227 (1997)
[22] Ma, W. X.: Methods appl. Anal.. 7, 21 (2000)
[23] Ma, W. X.; Fuchssteiner, B.: Phys. lett. A. 213, 49 (1996) · Zbl 0863.35106
[24] Ma, W. X.: Phys. lett. A. 316, 72 (2003)
[25] Ma, W. X.: J. math. Phys.. 46, 033507 (2005)
[26] Ma, W. X.; Xu, X. X.; Zhang, Y. F.: J. math. Phys.. 47, 053501 (2006)
[27] Ma, W. X.; Xu, X. X.; Zhang, Y. F.: Phys. lett. A. 351, 125 (2006)
[28] Ma, W. X.; Zhou, R. G.: Chin. ann. Math. ser. B. 23, 373 (2002)
[29] Ablowitz, M. J.; Kaup, D. J.; Newell, A. C.; Segur, H.: Stud. appl. Math.. 53, 249 (1974)