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By using a dynamical system method, in this paper studied are some exact traveling wave solutions and dynamic behaviors of these traveling wave solutions for simplified model of Gross-Pitaevskii (GP) equation in the 1D-Tonks-Girardeau gas. The effects of the behaviors on the parameters of the systems are also studied. Under different parametric conditions, six exact explicit parametric representations of the traveling wave solutions for simplified model of GP equation in the 1D-Tonks-Girardeau gas are given.
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Keywords:
- dynamical systems method /
- solitary wave solution /
- periodic wave solution /
- kink wave solution
[1] Girardeau M 1960 J. Math. Phys. 1 516
[2] Girardeau M 1965 Phys. Rev. B 139 500
[3] Tonks L 1936 Phys. Rev. 50 955
[4] Lieb E H, Liniger W 1963 Phys. Rev. 130 1605
[5] Olshanii M 1998 Phys. Rev. Lett. 81 938
[6] Dunjko V, Lorent V, Olshanii M 2001 Phys. Rev. Lett. 86 5413
[7] Paredes B, Widera A, Murg V 2004 Nature 429 227
[8] Kinoshita T, Wenger T, Weiss D 2004 Science 305 1125
[9] Kinoshita T, Wenger T, Weiss D 2006 Nature 440 900
[10] Pollet L, Rombouts S M, Denteneer P J 2004 Phys. Rev. Lett. 93 210401
[11] Rojo A, Cohen J L, Berman P R 1999 Phys. Rev. A 60 1482
[12] Girardeau M D, Wright E M 2000 Phys. Rev. Lett. 84 5239
[13] Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404
[14] Liu J, Zhang C, Mark G, Niu Q 2003 Phys. Rev. A 73 13601
[15] Carr L D, Brand J 2004 Phys. Rev. Lett. 92 40401
[16] Eiermann B, Anker T, Albiez M, Taglieber M, Treutlein P, Marzlin K P, Oberthaler M K 2004 Phys. Rev. Lett. 92 230401
[17] Jackson B, Proukakis N P, Barenghi C F 2007 Phys. Rev. A 75 51601
[18] Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K 1999 Phys. Rev. Lett. 83 5198
[19] Ei G A, Gammal A, Kamchatnov A M 2006 Phys. Rev. Lett. 97 180405
[20] Khawaja U A, Stoof H T C, Hulet R G, Strecker K E, Partridge G B 2000 Phys. Rev. Lett. 89 200404
[21] Prez-Garca V M, Michinel H, Herrero H 1998 Phys. Rev. A 57 3837
[22] Liu H, Wei J Y, Lou S Y, He X T 2008 Acta Phys. Sin. 57 1343 (in Chinese) [刘红, 魏佳羽, 楼森岳, 贺贤土 2008 57 1343]
[23] Lee T D, Huang K, Yang C N 1957 Phys. Rev. 106 1135
[24] Li J B, Dai H H 2007 On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach (Beijing: Science Press) p19
[25] Li J B 2008 Appl. Math. Mech. 29 1261 (in Chinese) [李继彬 2008 应用数学和力学 29 1261]
[26] Li J B, Liu Z R 2000 Appl. Math. Model. 25 41
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[1] Girardeau M 1960 J. Math. Phys. 1 516
[2] Girardeau M 1965 Phys. Rev. B 139 500
[3] Tonks L 1936 Phys. Rev. 50 955
[4] Lieb E H, Liniger W 1963 Phys. Rev. 130 1605
[5] Olshanii M 1998 Phys. Rev. Lett. 81 938
[6] Dunjko V, Lorent V, Olshanii M 2001 Phys. Rev. Lett. 86 5413
[7] Paredes B, Widera A, Murg V 2004 Nature 429 227
[8] Kinoshita T, Wenger T, Weiss D 2004 Science 305 1125
[9] Kinoshita T, Wenger T, Weiss D 2006 Nature 440 900
[10] Pollet L, Rombouts S M, Denteneer P J 2004 Phys. Rev. Lett. 93 210401
[11] Rojo A, Cohen J L, Berman P R 1999 Phys. Rev. A 60 1482
[12] Girardeau M D, Wright E M 2000 Phys. Rev. Lett. 84 5239
[13] Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404
[14] Liu J, Zhang C, Mark G, Niu Q 2003 Phys. Rev. A 73 13601
[15] Carr L D, Brand J 2004 Phys. Rev. Lett. 92 40401
[16] Eiermann B, Anker T, Albiez M, Taglieber M, Treutlein P, Marzlin K P, Oberthaler M K 2004 Phys. Rev. Lett. 92 230401
[17] Jackson B, Proukakis N P, Barenghi C F 2007 Phys. Rev. A 75 51601
[18] Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K 1999 Phys. Rev. Lett. 83 5198
[19] Ei G A, Gammal A, Kamchatnov A M 2006 Phys. Rev. Lett. 97 180405
[20] Khawaja U A, Stoof H T C, Hulet R G, Strecker K E, Partridge G B 2000 Phys. Rev. Lett. 89 200404
[21] Prez-Garca V M, Michinel H, Herrero H 1998 Phys. Rev. A 57 3837
[22] Liu H, Wei J Y, Lou S Y, He X T 2008 Acta Phys. Sin. 57 1343 (in Chinese) [刘红, 魏佳羽, 楼森岳, 贺贤土 2008 57 1343]
[23] Lee T D, Huang K, Yang C N 1957 Phys. Rev. 106 1135
[24] Li J B, Dai H H 2007 On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach (Beijing: Science Press) p19
[25] Li J B 2008 Appl. Math. Mech. 29 1261 (in Chinese) [李继彬 2008 应用数学和力学 29 1261]
[26] Li J B, Liu Z R 2000 Appl. Math. Model. 25 41
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