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A class of disturbed evolution equation is considered by a simple and valid technique. We first introduce the traveling solitary wave solution of a corresponding typical differential equation, and then use the asymptotic method to obtain the approximate solution for an original disturbed evolution equation. And we point out that the series of approximate solution is convergent and the precision of the approximate solution is discussed by using the fixed point theorem for the functional analysis.
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Keywords:
- nonlinear /
- evolution equation /
- asymptotic method
[1] Ma Songhua, Qiang Jiye, Fang Jianping, Annihilation 2007 Commum. Theor. Phys. 48 662
[2] Parkes J 2008 Chaos Solitons Fractals 38 154
[3] Yang J R, Mao J J 2008 Chin. Phys. Lett. 25 1527
[4] Yang X D, Ruan H Y, Lou S Y 2007 Commum. Theor. Phys. 48 961
[5] Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[6] Yang Z, Ma S H, Fang J P 2011 Acta Phys. Sin. 60 040508 (in Chinese) [杨征, 马松华, 方建平 2011 60 040508]
[7] Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 54 290]
[8] Bartier Jean-Philippe 2006 Asymptotic Anal. 46 325
[9] Libre J, da Silva P R, Teixeira M A 2007 J. Dyn. Differ. Equations 19 309
[10] Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[11] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York, CRC Press)
[12] Mo J Q 2009 Chin Phys. Lett. 26 060202
[13] Mo J Q 2010 Commun. Theor. Phys. 53 440
[14] Mo J Q, Lin W T, Lin Y H 2011 Acta Phys. Sin. 60 080202 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2011 60 080202]
[15] Mo J Q 2009 Science in China, Ser G 39 568
[16] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[17] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[18] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[19] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation, (Amsterdam: North-Holland Publishing)
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[1] Ma Songhua, Qiang Jiye, Fang Jianping, Annihilation 2007 Commum. Theor. Phys. 48 662
[2] Parkes J 2008 Chaos Solitons Fractals 38 154
[3] Yang J R, Mao J J 2008 Chin. Phys. Lett. 25 1527
[4] Yang X D, Ruan H Y, Lou S Y 2007 Commum. Theor. Phys. 48 961
[5] Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[6] Yang Z, Ma S H, Fang J P 2011 Acta Phys. Sin. 60 040508 (in Chinese) [杨征, 马松华, 方建平 2011 60 040508]
[7] Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 54 290]
[8] Bartier Jean-Philippe 2006 Asymptotic Anal. 46 325
[9] Libre J, da Silva P R, Teixeira M A 2007 J. Dyn. Differ. Equations 19 309
[10] Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[11] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York, CRC Press)
[12] Mo J Q 2009 Chin Phys. Lett. 26 060202
[13] Mo J Q 2010 Commun. Theor. Phys. 53 440
[14] Mo J Q, Lin W T, Lin Y H 2011 Acta Phys. Sin. 60 080202 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2011 60 080202]
[15] Mo J Q 2009 Science in China, Ser G 39 568
[16] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[17] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[18] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[19] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation, (Amsterdam: North-Holland Publishing)
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