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New integrable systems of derivative nonlinear Schrödinger equations with multiple components. (English) Zbl 0936.37043
Summary: The Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schrödinger equation proposed by Kaup-Newell is also obtained.

37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q55NLS-like (nonlinear Schrödinger) equations
Full Text: DOI
[1] Kaup, D. J.; Newell, A. C.: J. math. Phys.. 19, 798 (1978)
[2] Chen, H. H.; Lee, Y. C.; Liu, C. S.: Phys. scr.. 20, 490 (1979)
[3] Wadati, M.; Sogo, K.: J. phys. Soc. jpn.. 52, 394 (1983)
[4] Kundu, A.: J. math. Phys.. 25, 3433 (1984)
[5] M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991. · Zbl 0762.35001
[6] Manakov, S. V.: Sov. phys. JETP. 38, 248 (1974)
[7] Fordy, A. P.; Kulish, P. P.: Commun. math. Phys.. 89, 427 (1983)
[8] Yajima, N.; Oikawa, M.: Prog. theor. Phys.. 54, 1576 (1975)
[9] Tsuchida, T.; Wadati, M.: J. phys. Soc. jpn.. 67, 1175 (1998)
[10] Tsuchida, T.; Ujino, H.; Wadati, M.: J. math. Phys.. 39, 4785 (1998)
[11] Tsuchida, T.; Ujino, H.; Wadati, M.: J. phys. A. 32, 2239 (1999)
[12] Morris, H. C.; Dodd, R. K.: Phys. scr.. 20, 505 (1979)
[13] Fordy, A. P.: J. phys. A. 17, 1235 (1984)
[14] Yajima, T.: J. phys. Soc. jpn.. 64, 1901 (1995)
[15] Svinolupov, S. I.: Commun. math. Phys.. 143, 559 (1992)
[16] Svinolupov, S. I.: Func. anal. Appl.. 27, 257 (1993)
[17] Svinolupov, S. I.; Sokolov, V. V.: Theor. math. Phys.. 100, 959 (1994)
[18] I.T. Habibullin, V.V. Sokolov, R.I. Yamilov, Multi-component integrable systems and nonassociative structures, in Nonlinear Physics: Theory and Experiment, World Scientific, Singapore, 1996, p. 139. · Zbl 0941.37523
[19] Olver, P. J.; Sokolov, V. V.: Commun. math. Phys.. 193, 245 (1998)
[20] M. Hisakado, Chiral solitons from dimensional reduction of Chern--Simons gauged coupled non-linear Schrödinger model, hep-th/9712255.
[21] Ablowitz, M. J.; Kaup, D. J.; Newell, A. C.; Segur, H.: Phys. rev. Lett.. 31, 125 (1973)
[22] Zakharov, V. E.; Shabat, A. B.: Func. anal. Appl.. 8, 226 (1974)
[23] Ablowitz, M. J.; Haberman, R.: J. math. Phys.. 16, 230 (1975)
[24] Wadati, M.; Konno, K.; Ichikawa, Y.: J. phys. Soc. jpn.. 46, 1965 (1979)
[25] Tsuchida, T.; Wadati, M.: J. phys. Soc. jpn.. 65, 3153 (1996)