Abstract
Based on the generalized dressing method, we propose integrable variable coefficient coupled cylindrical nonlinear Schrödinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agrawal, G.P., Boyd, R.W. Nonlinear Fiber Optics. Springer-Verlag, New York, 2001
Agrawal, G.P. Nonlinear and Fiber Optics. Acadmic Press, London, 1989
Benney, D.J., Newell, A.C. The propagation of nonlinear wave envelopes. J. Math. Phys., 46: 133–139 (1967)
Benney, D.J., Roskes, G.J. Wave instabilities. Stud. Appl. Math., 48: 377–385 (1969)
Buryak, A.V., Kivshar, Y.S., Parker, D.F. Coupling between dark and bright solitons. Phys. Lett. A., 215: 57–62 (1996)
Chowdhury, A.R., Basak, B. On the complete solution of the Hirota-Satsuma system through the ‘dressing’ operator technique. J. Phys. A., 17: L863–L868 (1984)
Christodoulides, D.N., Coskun, T.H., Mitchell, M., Segev, M. Theory of Incoherent Self-focusing in Biased Photorefractive Media. Phys. Rev. Lett., 78: 646–649 (1997)
Dai, H.H., Jeffrey, A. The inverse scattering transforms for certain types of variable-coefficient KdV equations. Phys. Lett. A., 139: 369–372 (1989)
Dye, J.M., Parker, A. An inverse scattering scheme for the regularized long-wave equation. J. Math. Phys. 41: 2889–2904 (2000)
Hasegawa, A. Generation of a train of soliton pulses by induced modulational instability in optical fibers. Optics Letters, 9: 288–290 (1984)
Jeffrey, A., Dai, H.H. On the application of a generalizzed version of the dressing method to the integration of variable-coefficient KdV equation. Rendiconti.di Mathematica, Serie VII. 10: 439–455 (1990)
Parker, A. A reformulation of the ‘dressing method’ for the Sawada-Kotera equation. Inverse Problems, 17: 885–895 (2001)
Porsezian, K., Shanmugha, S.P., Mahalingam, A. Coupled high-order nonlinear Schrödinger equations in nonlinear optics:Painlevé analysis and integrability. Phys. Rev. E, 50: 1543–1547 (1994)
SaSa, N., Satsuma, J. New-type of soliton solutions for a higher-order nonlinear Schrödinger equation. J. Phys. Soc. Jpn., 60: 409–417 (1991)
Tasgal, R.S., Potasek, M.J. Soliton solutions to coupled higher-order nonlinear Schrödinger equations. J. Math. Phys., 33: 1028–1215 (1992)
Zakharov, V.E., Shabat, A.B. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem I. Funt. Anal. Appl., 8: 226–235 (1974)
Zakharov, V.E., Shabat, A.B. Integration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem II. Funt. Anal. Appl., 13: 166–174 (1979)
Zakharov, V.E., Shabat, A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP., 34: 62–69 (1972)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by a grant from City University of Hong Kong (Project No: 7002366). The authors acknowledge the support by National Natural Science Foundation of China (Project No: 11301149)and Henan Natural Science Foundation For Basic Research under Grant No:132300410310. Doctor Foundation of Henan Institute of Engeering under Grant No: D2010007.
Rights and permissions
About this article
Cite this article
Su, T., Ding, Gh. & Fang, Jy. Integrable variable-coefficient coupled cylindrical NLS equations and their explicit solutions. Acta Math. Appl. Sin. Engl. Ser. 30, 1017–1024 (2014). https://doi.org/10.1007/s10255-014-0439-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-014-0439-z