Abstract
With the help of the similarity transformation and the solvable stationary nonlinear Schrödinger equation (NLSE), we obtain exact chirped and chirp-free self-similar cnoidal wave and solitary wave solutions of the generalized NLSE exhibiting spatial inhomogeneity, inhomogeneous nonlinearity and gain or loss at the same time. As an example, we investigate their propagation dynamics in a nonlinear optical system, and present a series of interesting properties of optical waves.
Similar content being viewed by others
References
T.M. Monro, D. Moss, M. Bazylenko, C. Martijn de Sterke, L. Poladian, Phys. Rev. Lett. 80, 4072 (1998)
M.E. Fermann, V.I. Kruglov, B.C. Thomsen, J.M. Dudley, J.D. Harvey, Phys. Rev. Lett. 84, 6010 (2000)
F.Ö. Ilday, J.R. Buckley, W.G. Clark, F.W. Wise, Phys. Rev. Lett. 92, 213902 (2004)
S.A. Ponomarenko, G.P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006)
V.I. Kruglov, A.C. Peacock, J.D. Harvey, Phys. Rev. E 71, 056619 (2005)
S.H. Chen, L. Yi, Phys. Rev. E 71, 016606 (2005)
K. Senthilnathan, Q. Li, K. Nakkeeran, P.K.A. Wai, Phys. Rev. A 78, 033835 (2008)
S. Pitois, J. Fatome, G. Millot, Opt. Lett. 27, 1729 (2002)
A. Hasegawa, Opt. Lett. 9, 288 (1984)
K. Tai, A. Tomita, J.L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986)
H.A. Haus, IEEE J. Sel. Top. Quant. Electron. 6, 1173 (2000)
V.M. Petnikova, V.V. Shuvalov, V.A. Vysloukh, Phys. Rev. E 60, 1009 (1999)
R.Y. Hao, G.S. Zhou, Opt. Commun. 281, 4474 (2008)
L. Wu, J.F. Zhang, L. Li, Q. Tian, K. Porsezian, Opt. Express 16, 6352 (2008)
V.M. Pérez-García, P. Torres, V.V. Konotop, Physica D 221, 31 (2006)
V. Serkin, A. Hasegawa, T.S. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007)
B. Li, X.F. Zhang, Y.Q. Li, Y. Chen, W.M. Liu, Phys. Rev. A 78, 023608 (2008)
J.K. Xue, J. Phys. B: At. Mol. Opt. Phys. 38, 3841 (2005)
Z.X. Liang, Z.D. Zhang, W.M. Liu, Phys. Rev. Lett. 94, 050402 (2005)
J. Belmonte-Beitia, V.M. Pérez-García, V. Vekslerchik, V.V. Konotop, Phys. Rev. Lett. 100, 16410 (2008)
J.D. Moores, Opt. Lett. 21, 555 (1996)
V.N. Serkin, A. Hasegawa, Phys. Rev. Lett. 85, 4502 (2000)
V.I. Kruglov, A.C. Peacock, J.D. Harvey, Phys. Rev. Lett. 90, 113902 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, L., Dai, C. Self-similar cnoidal and solitary wave solutions of the (1+1)-dimensional generalized nonlinear Schrödinger equation. Eur. Phys. J. D 58, 327–332 (2010). https://doi.org/10.1140/epjd/e2010-00102-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2010-00102-0