AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schrödinger equations

Journal of Mathematical Physics - Tập 52 Số 4 - 2011
Dun Zhao1,2, Yujuan Zhang1, Wei-Wei Lou1, Hong‐Gang Luo2,3
1Lanzhou University 1 School of Mathematics and Statistics, , Lanzhou 730000, China
2Lanzhou University 2 Center for Interdisciplinary Studies, , Lanzhou 730000, China
3Lanzhou University 3 Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, , Lanzhou 730000, China

Tóm tắt

By constructing nonisospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schrödinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose–Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.

Từ khóa


Tài liệu tham khảo

2006, Soliton Management in Periodic Systems

2000, Science, 287, 97, 10.1126/science.287.5450.97

Kevrekidis, 2008, Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment, 10.1007/978-3-540-73591-5

2002, Nature, 417, 150, 10.1038/nature747

2002, Science, 296, 1290, 10.1126/science.1071021

1980, Phys. Rev. Lett., 45, 1095, 10.1103/PhysRevLett.45.1095

1995, Solitons in Optical Communications

2000, Chaos, 10, 486, 10.1063/1.1311394

2006, Solitons in Optical Fibers

2000, Phys. Rev. Lett., 85, 4502, 10.1103/PhysRevLett.85.4502

2000, JETP Lett., 72, 89, 10.1134/1.1312019

2001, JETP Lett., 74, 573, 10.1134/1.1455063

2002, IEEE J. Sel. Top. Quantum Electron., 8, 418, 10.1109/JSTQE.2002.1016344

2004, Phys. Rev. Lett., 92, 199401, 10.1103/PhysRevLett.92.199401

2007, Phys. Rev. Lett., 98, 074102, 10.1103/PhysRevLett.98.074102

2010, Phys. Rev. A, 81, 023610, 10.1103/PhysRevA.81.023610

2005, Phys. Rev. Lett., 94, 050402, 10.1103/PhysRevLett.94.050402

2003, Phys. Rev. Lett., 90, 113902, 10.1103/PhysRevLett.90.113902

2004, Phys. Rev. Lett., 92, 199402, 10.1103/PhysRevLett.92.199402

2008, Phys. Lett. A, 372, 5644, 10.1016/j.physleta.2008.07.013

2009, Eur. Phys. J. D, 53, 213, 10.1140/epjd/e2009-00051-7

2009, Phys. Rev. E, 79, 056610, 10.1103/PhysRevE.79.056610

2009, Phys. Rev. A, 79, 063802, 10.1103/PhysRevA.79.063802

2009, Phys. Rev. A, 80, 063626, 10.1103/PhysRevA.80.063626

2009, Phys. Rev. A, 79, 023619, 10.1103/PhysRevA.79.023619

2009, Phys. Rev. A, 79, 013423, 10.1103/PhysRevA.79.013423

1972, Sov. Phys. JETP, 34, 62

1974, Teor. Mat. Fiz., 19, 332, 10.1007/BF01035568

1974, Teor. Mat. Fiz., 6, 68

1974, Stud. Appl. Math., 53, 249, 10.1002/sapm1974534249

1976, Phys. Rev. Lett., 37, 693, 10.1103/PhysRevLett.37.693

1982, Phys. Lett. A, 92, 243, 10.1016/0375-960(82)90027-5

1985, Phys. Rev. A, 32, 1144, 10.1103/PhysRevA.32.1144

2005, Darboux Transformations in Integrable Systems

1975, Prog. Theor. Phys., 53, 419, 10.1143/PTP.53.419

2006, Introduction to Soliton Theory

2010, AIP Conf. Proc., 1212, 213, 10.1063/1.3367048

Thông tin
Thông tin xuất bản

Journal of Mathematical Physics

Tập 52 Số 4

Thông tin tác giả