Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations

• Authors: İ. Aslan
• Languages of publication: EN

Abstracts

EN

Nonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.

Keywords

EN

02.30.Jr   02.30.Hq   04.20.Jb  

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 123
• Issue: 1
• Pages: 16-20

Dates

published

2013-01

received

2012-05-28

(unknown)

2012-10-22

References

• [1] J. Weiss, M. Tabor, G. Carnevale, J. Math. Phys. 24, 522 (1983)
• [2] M.J. Ablowitz, H. Segur, Solitons and Inverse Scattering Transform, SIAM, Philadelphia 1981
• [3] A.M. Wazwaz, Appl. Math. Comput. 201, 489 (2008)
• [4] W.X. Ma, Chaos Solitons Fract. 42, 1356 (2009)
• [5] G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York 1989
• [6] A.M. Wazwaz, Appl. Math. Comput. 154, 713 (2004)
• [7] M.L. Wang, Phys. Lett. A 213, 279 (1996)
• [8] M.A. Abdou, Chaos Solitons Fract. 31, 95 (2007)
• [9] M. Wang, X. Li, J. Zhang, Phys. Lett. A 372, 417 (2008)
• [10] J.H. He, X.H. Wu, Chaos Solitons Fract. 30, 700 (2006)
• [11] J.H. He, Appl. Math. Comput. 151, 287 (2004)
• [12] A. Biswas, H. Triki, Appl. Math. Comput. 217, 3869 (2010)
• [13] D. Wang, H.Q. Zhang, Chaos Solitons Fract. 25, 601 (2005)
• [14] W.X. Ma, T. Huang, Y. Zhang, Phys. Scr. 82, 065003 (2010)
• [15] M. Dehghan, A. Hamidi, M. Shakourifar, Appl. Math. Comput. 189, 1034 (2007)
• [16] W.X. Ma, Y. Zhang, Y. Tang, J. Tu, Appl. Math. Comput. 218, 7174 (2012)
• [17] Z. Feng, Phys. Lett. A. 293, 57 (2002)
• [18] Z. Feng, X. Wang, Phys. Scr. 64, 7 (2001)
• [19] Z. Feng, J. Phys. A, Math. Gen. 35, 343 (2002)
• [20] X. Deng, Appl. Math. Comput. 204, 733 (2008)
• [21] Z. Feng, S. Zheng, D.Y. Gao, Z. Angew. Math. Phys. 60, 756 (2009)
• [22] Naranmandula, K.X. Wang, Chin. Phys. 13, 139 (2004)
• [23] Z. Feng, R. Knobel, J. Math. Anal. Appl. 328, 1435 (2007)
• [24] İ. Aslan, Appl. Math. Comput. 217, 8134 (2011)
• [25] S. Abbasbandy, A. Shirzadi, Commun. Nonlinear Sci. Numer Simul. 15, 1759 (2010)
• [26] K.R. Raslan, Nonlinear Dyn. 53, 281 (2006)
• [27] İ. Aslan, Pramana-J. Phys. 76, 1 (2011)
• [28] T.R. Ding, C.Z. Li, Ordinary Differential Equations, Peking University Press, Peking 1996
• [29] Z. Feng, Electron J. Linear Algebra 8, 14 (2001)
• [30] N. Bourbaki, Commutative Algebra, Addison-Wesley, Paris 1972
• [31] C.Q. Bian, J. Pang, L.H Jin, X.M. Ying, Commun. Nonlinear Sci. Numer. Simul. 15, 2337 (2010)
• [32] W.X. Ma, J. Phys. A, Math. Gen. 26, L17 (1993)
• [33] W.X. Ma, M. Chen, Appl. Math. Comput. 215, 2835 (2009)
• [34] A. Biswas, S. Konar, Introduction to Non-Kerr Law Optical Solitons, CRC Press, Florida 2007

Identifiers

DOI

10.12693/APhysPolA.123.16