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The investigation of nonlinear wave propagation in cylindrical shells is of theoretical and realistic significance. In this work, using homotopy analysis method, we study a new model of nonlinear wave propagation in inhomogeneous cylindrical shells, and obtain approximate solitary wave solution and periodic wave solution with high accuracy. It shows that homotopy analysis method is one of the most effective methods for research into the problems of nonlinear wave propagation.
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Keywords:
- homotopy analysis method /
- cylindrical shells /
- solitary wave /
- periodic wave
[1] ［1］Liao S J 2006 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Beijing: Science Press) (in Chinese) ［廖世俊 2006 超越摄动——同伦分析方法导论（北京：科学出版社）］
[2] ［2］Liao S J 2004 Appl. Math. Comput. 147 499
[3] ［3］Shi Y R, Xu X J, Wu Z X, Wang Y H, Yang H J, Duan W S, Lü K P 2006 Acta Phys. Sin. 55 1555 (in Chinese) ［石玉仁、许新建、吴枝喜、汪映海、杨红娟、段文山、吕克璞 2006 物理学报 55 1555］
[4] ［4］Yang H J, Shi Y R, Duan W S, Lü K P 2007 Acta Phys. Sin. 56 3064 (in Chinese) ［杨红娟、石玉仁、段文山、吕克璞 2007 物理学报 56 3064］
[5] ［5］Shi Y R, Wang Y H, Yang H J, Duan W S 2007 Acta Phys. Sin. 56 6791(in Chinese) ［石玉仁、汪映海、杨红娟、段文山 2007 物理学报 56 6791］
[6] ［6］Wu Q K, 2008 Acta Phys. Sin. 57 2654 (in Chinese) ［吴钦宽 2008 物理学报 57 2654］
[7] ［7］Rashidi M M, Domairry G, Dinarvand S 2009 Communications in Nonlinear Science and Numerical Simulation 14 708
[8] ［8］Jiao X Y, Gao Y, Lou S Y 2009 Sci. China Ser. G 52 1169
[9] ［9］Novozhilov V V 1962 The theory of thin shells (Leningrad: Sudpromgiz)
[10] ］Vol’mir A S 1972 Nonlinear dynamics of plates and shells (Moscow: Nauka)
[11] ］Zemlyanukhin A I, Mogilevich L I 2001 Acoustical Physics 47 303
[12] ］Zemlyanukhin A I, Mogilevich L I 1999 Nonlinear waves in cylindrical shells (Saratov: Saratov University Press)
[13] ］Lu D Z 2005 Acta Phys. Sin. 54 4501 (in Chinese) ［吕大昭 2005 物理学报 54 4501］
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[1] ［1］Liao S J 2006 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Beijing: Science Press) (in Chinese) ［廖世俊 2006 超越摄动——同伦分析方法导论（北京：科学出版社）］
[2] ［2］Liao S J 2004 Appl. Math. Comput. 147 499
[3] ［3］Shi Y R, Xu X J, Wu Z X, Wang Y H, Yang H J, Duan W S, Lü K P 2006 Acta Phys. Sin. 55 1555 (in Chinese) ［石玉仁、许新建、吴枝喜、汪映海、杨红娟、段文山、吕克璞 2006 物理学报 55 1555］
[4] ［4］Yang H J, Shi Y R, Duan W S, Lü K P 2007 Acta Phys. Sin. 56 3064 (in Chinese) ［杨红娟、石玉仁、段文山、吕克璞 2007 物理学报 56 3064］
[5] ［5］Shi Y R, Wang Y H, Yang H J, Duan W S 2007 Acta Phys. Sin. 56 6791(in Chinese) ［石玉仁、汪映海、杨红娟、段文山 2007 物理学报 56 6791］
[6] ［6］Wu Q K, 2008 Acta Phys. Sin. 57 2654 (in Chinese) ［吴钦宽 2008 物理学报 57 2654］
[7] ［7］Rashidi M M, Domairry G, Dinarvand S 2009 Communications in Nonlinear Science and Numerical Simulation 14 708
[8] ［8］Jiao X Y, Gao Y, Lou S Y 2009 Sci. China Ser. G 52 1169
[9] ［9］Novozhilov V V 1962 The theory of thin shells (Leningrad: Sudpromgiz)
[10] ］Vol’mir A S 1972 Nonlinear dynamics of plates and shells (Moscow: Nauka)
[11] ］Zemlyanukhin A I, Mogilevich L I 2001 Acoustical Physics 47 303
[12] ］Zemlyanukhin A I, Mogilevich L I 1999 Nonlinear waves in cylindrical shells (Saratov: Saratov University Press)
[13] ］Lu D Z 2005 Acta Phys. Sin. 54 4501 (in Chinese) ［吕大昭 2005 物理学报 54 4501］
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