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Volumn 42, Issue 2, 2004, Pages 161-170

A new class of (2+1)-dimensional localized coherent structures with completely elastic and non-elastic interactive properties

Author keywords

(2+1) dimensional localized coherent structures; Soliton; Variable separation method

Indexed keywords


EID: 4444324057     PISSN: 02536102     EISSN: None     Source Type: Journal    
DOI: 10.1088/0253-6102/42/2/161     Document Type: Article
Times cited : (19)

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    • (2002) Phys. Scr. , vol.65 , pp. 7
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    • Lou, S.Y.1    Ruan, H.Y.2
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    • Hong, K.Z.1    Wu, B.2    Chen, X.F.3
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    • Tang, X.Y.1    Lou, S.Y.2
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    • 0034693656 scopus 로고    scopus 로고
    • in Chinese
    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
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    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
    • (2002) Commun. Theor. Phys. (Beijing, China) , vol.38 , pp. 1
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    • in Chinese
    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
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    • (2003) Commun. Theor. Phys. (Beijing, China) , vol.40 , pp. 401
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    • (2003) Commun. Theor. Phys. (Beijing, China) , vol.40 , pp. 533
    • Zhang, J.F.1    Huang, W.H.2
  • 35
    • 0034693656 scopus 로고    scopus 로고
    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
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    • Zhang, J.F.1    Zheng, C.L.2    Meng, J.P.3    Fang, J.P.4
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    • 0034693656 scopus 로고    scopus 로고
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    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
    • (2003) Phys. Lett. A
    • Zhang, J.F.1
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    • 0034693656 scopus 로고    scopus 로고
    • in Chinese
    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
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    • 0034693656 scopus 로고    scopus 로고
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    • S.Y. Lou, Phys. Lett. A277 (2000) 94; X.Y. Tang and S.Y. Lou, Chaos, Solitons and Fractals 14 (2002) 1451; S.Y. Lou, C.L. Chen, and X.Y. Tang, J. Math. Phys. 43 (2002) 4078; S.Y. Lou and J.Z. Lu, J. Phys. A: Math. Gen. 29 (1996) 4029; S.Y. Lou, Phys. Scr. 65 (2002) 7; X.Y. Tang, C.L. Chen, and S.Y. Lou, J. Phys. A: Math. Gen. 35 (2002) L293; S.Y. Lou and H.Y. Ruan, J. Phys. A: Math. Gen. 30 (2001) 305; S.Y. Lou, Physica Scripta 65 (2002) 7; S.Y. Lou, X.Y. Tang, and C.L. Chen, Chin. Phys. Lett. 19 (2002) 769; K.Z. Hong, B. Wu, and X.F. Chen, Commun. Theor. Phys. (Beijing, China) 39 (2003) 393; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 20 (2003) 335; H.Y. Ruan and Y.X. Chen, Acta Phys. Sin. 50 (2001) 586 (in Chinese); X.Y. Tang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 38 (2002) 1; H.Y. Ruan and Y.X. Chen, Acta. Phys. Sin. 52 (2003) 1313 (in Chinese); S.Y. Lou, J. Phys. A: Math. Gen. 36 (2003) 3877; S.L. Zhang and S.Y. Lou, Commun. Theor. Phys. (Beijing, China) 40 (2003) 401; J.F. Zhang and W.H. Huang, Commun. Theor. Phys. (Beijing, China) 40 (2003) 533; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 653; J.F. Zhang, Phys. Lett. A (2003) (in Press); J.F. Zhang and P. Han, Acta Phys. Sin. 51 (2002) 705 (in Chinese); J.F. Zhang, Chin. Phys. 10 (2001) 89; J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 38 (2002) 277; J.F. Zhang, Chin. Phys. 11 (2002) 651; J.F. Zhang, W.H. Huang, and C.L. Zhefig, Acta. Phys. Sin. 51 (2002) 2627 (in Chinese); J.F. Zhang, Phys. Lett. A313 (2003) 401; C.L. Zheng and J.F. Zhang, Chin. Phys. Lett. 19 (2002) 1399; C.L. Zheng, J.F. Zhang, and Z.M. Sheng, Chin. Phys. Lett. 20 (2003) 331; J.F. Zhang, C.L. Zheng, J.P. Meng, and J.P. Fang, Chin. Phys. Lett. 20 (2003) 448; C.L. Zheng, J.F. Zhang, W.H. Huang, and L.Q. Chen, Chin. Phys. Lett. 20 (2003) 783; C.L. Zheng, J.M. Zhu, and J.F. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 261; J.F. Zhang and J.P. Meng, Chin. Phys. Lett. 20 (2003) 1006; H.Y. Ruan and Y.X. Chen, Chaos, Solitons and Fractals 17 (2003) 929.
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