非线性波动系统的冲击层解
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摘要
考虑非线性奇异摄动波动方程第三边值问题,先利用奇异摄动法构造外部解,再引入伸长变量依次得到解的冲击波尖层、初始层及边界层的校正项,最后给出问题解的渐近展开式,并证明渐近解的一致有效性.
We considered the third boundary value problem of nonlinear singularly perturbed wave equation.Firstly,the outer solution was constructed by using singular perturbation method.Secondly,correction terms of the shock layer,initial layer and boundary layer were obtained by using the stretched variables.Finally,the asymptotic expansion of solution to problem was given,and the uniform validity of its asymptotic solution was proved.
We considered the third boundary value problem of nonlinear singularly perturbed wave equation.Firstly,the outer solution was constructed by using singular perturbation method.Secondly,correction terms of the shock layer,initial layer and boundary layer were obtained by using the stretched variables.Finally,the asymptotic expansion of solution to problem was given,and the uniform validity of its asymptotic solution was proved.
引文
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[11]莫嘉琪.一类非线性尘埃等离子体孤波解[J].物理学报,2011,60(3):030203-1-030203-4.(MO Jiaqi.The Solution for a Class of Nonlinear Solitary Waves in Dusty Plasma[J].Acta Phys Sin,2011,60(3):030203-1-030203-4.)
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[14]MO Jiaqi,LIN Wantao.Generalized Variation Iteration Solution of an Atmosphere-Ocean Oscillator Model for Global Climate[J].J Sys Sci Compl,2011,24(2):271-276.
[15]CHEN Huaijun,SHI Lanfang,MO Jiaqi.A Generalized Interior Shock Layer Solution to Nonlinear Singularly Perturbed Equations[J].J Univ Sci Tech China,2015,45(8):638-642.
[16]CHEN Huaijun.Perturbed Problem for a Class of Reaction Diffusion with Time Delay[J].J Anhui Normal Univ(Nat Sci),2011,34(6):511-515.
[17]XU Jianzhong,ZHOU Zongfu.Existence and Uniqueness of Anti-periodic Solutions to an nth-Order Nonlinear Differential Equation with Multiple Deviating Arguments[J].Ann Diff Eqs,2012,28(1):105-114.
[18]XU Jianzhong,ZHOU Zongfu.Anti-periodic Solutions for a Kind of Nonlinear nth-Order Differential Equation with Multiple Deviating Arguments[J].J Chongqing Technol Business Univ(Nat Sci Ed),2010,27(6):545-550.
[2]ZHAO Baojun,WANG Ruyun,SUN Wenjin,et al.Combined ZK-mZK Equation for Rossby Solitary Waves with Complete Coriolis Force and Its Conservation Laws as Well as Exact Solutions[J/OL].Adv Diff Equ,2018-01-25.http://doi.org/10.1186/s13662-018-1492-3.
[3]刘芝镗,斯仁道尔吉.变系数Zakhsrov-Kuznetsov方程的类周期孤波解[J].应用数学,2018,31(1):55-59.(LIU Zhitang,Sirendaoerji.Periodic Solitary-Like Wave Solutions of Variable-Coefficient Zakharov-Kuznetsov Equation[J].Math Appl,2018,31(1):55-59.)
[4]谢怡,王砚.高度非线性孤立波与弹性大板的耦合作用研究[J].固体力学学报,2017,38(1):65-73.(XIE Yi,WANG Yan.The Coupling Mechanism between Highly Nonlinear Solitary Waves with Large Plate[J].Chin JSolid Mech,2017,38(1):65-73.)
[5]何章明,张志强.玻色-爱因斯坦凝聚体中的双孤子相互作用操控[J].物理学报,2016,65(11):110502-1-110502-6.(HE Zhangming,ZHANG Zhiqiang.Controlling Interactions between Bright Solitons in Bose-Einstein Condensate[J].Acta Phys Sin,2016,65(11):110502-1-110502-6.)
[6]蔺福军,廖晶晶,朱云.q-非广延分布等离子体中的离子声孤波[J].天文学报,2015,56(1):17-25.(LIN Fujun,LIAO Jingjing,ZHU Yun.Ion-Acoustic Solitary Waves in a q-Nonextensive Plasma[J].Acta Astronomica Sinica,2015,56(1):17-25.)
[7]吴钦宽.一类非线性扰动Burgers方程的孤子变分迭代解法[J].物理学报,2012,61(2):020203-1-020203-4.(WU Qinkuan.Variational Iteration Solution Method of Soliton for a Class of Nonlinear Disturbed Burgers Equation[J].Acta Phys Sin,2012,61(2):020203-1-020203-4.)
[8]MO Jiaqi.Homotopic Mapping Solving Method for Gain Fluency of a Laser Pulse Amplifier[J].Sci in Chin Ser G:Phy,Mech Astron,2009,52(7):1007-1010.
[9]MO Jiaqi,LIN Shurong.The Homotopic Mapping Solution for the Solitary Wave for a Generalized Nonlinear Evolution Equation[J].Chin Phys B,2009,18(9):3628-3631.
[10]MO Jiaqi,LIN Wantao,LIN Yihua.Asymptotic Solution for the El Nino Time Delay Sea-Air Oscillator Model[J].Chin Phys B,2011,20(7):070205-1-070205-6.
[11]莫嘉琪.一类非线性尘埃等离子体孤波解[J].物理学报,2011,60(3):030203-1-030203-4.(MO Jiaqi.The Solution for a Class of Nonlinear Solitary Waves in Dusty Plasma[J].Acta Phys Sin,2011,60(3):030203-1-030203-4.)
[12]MO Jiaqi,LIN Yihua,LIN Wantao,et al.Perturbed Solving Method for Interdecadal Sea-Air Oscillator Model[J].Chin Geogra Sci,2012,22(1):42-47.
[13]MO Jiaqi.Solution of Travelling Wave for Nonlinear Disturbed Long-Wave System[J].Commun Theor Phys,2011,55(3):387-390.
[14]MO Jiaqi,LIN Wantao.Generalized Variation Iteration Solution of an Atmosphere-Ocean Oscillator Model for Global Climate[J].J Sys Sci Compl,2011,24(2):271-276.
[15]CHEN Huaijun,SHI Lanfang,MO Jiaqi.A Generalized Interior Shock Layer Solution to Nonlinear Singularly Perturbed Equations[J].J Univ Sci Tech China,2015,45(8):638-642.
[16]CHEN Huaijun.Perturbed Problem for a Class of Reaction Diffusion with Time Delay[J].J Anhui Normal Univ(Nat Sci),2011,34(6):511-515.
[17]XU Jianzhong,ZHOU Zongfu.Existence and Uniqueness of Anti-periodic Solutions to an nth-Order Nonlinear Differential Equation with Multiple Deviating Arguments[J].Ann Diff Eqs,2012,28(1):105-114.
[18]XU Jianzhong,ZHOU Zongfu.Anti-periodic Solutions for a Kind of Nonlinear nth-Order Differential Equation with Multiple Deviating Arguments[J].J Chongqing Technol Business Univ(Nat Sci Ed),2010,27(6):545-550.