变耗散系数的柱Burgers方程和球Burgers方程的精确解
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摘要
根据简化齐次平衡原则,导出一个由线性方程的解到一个具变耗散系数的柱Burgers方程解的非线性变换.该线性方程容许有指数函数形式的解,因而借助所导出的非线性变换,获得一个具变耗散系数的柱Burgers方程的精确解.完全类似地,也获得一个具变耗散系数的球Burgers方程的精确解.
Based on the simplified homogeneous balance principle, a nonlinear transformation that forms the solution of a linear equation to the solution of a cylindrical Burgers equation with variable dissipative coefficient has been derived. Since the linear equation admits an exponential type solution,substituting it into the nonlinear transformation derived here, we have had the exact solution of the cylindrical Burgers equation with variable dissipative coefficient. This method can be used to obtain the exact solution of a spherical Burgers equation with variable dissipative coefficient too.
Based on the simplified homogeneous balance principle, a nonlinear transformation that forms the solution of a linear equation to the solution of a cylindrical Burgers equation with variable dissipative coefficient has been derived. Since the linear equation admits an exponential type solution,substituting it into the nonlinear transformation derived here, we have had the exact solution of the cylindrical Burgers equation with variable dissipative coefficient. This method can be used to obtain the exact solution of a spherical Burgers equation with variable dissipative coefficient too.
引文
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[2]石玉仁,杨红娟,段文山,等.柱Burgers方程和球Burgers方程的解析解[J].西北师范大学学报(自然科学版),2007,4:011.
[3]WANG M,LI X.Simplified homogeneous balance method and its applications to the whitham-BroerKaup model equations[J].Journal of Applied Mathematics and Physics,2014,2(08):823.
[4]WANG M.Solitary wave solutions for variant Boussinesq equations[J].Physics letters A,1995,199(3):169-172.
[5]WANG M,ZHOU Y,LI Z.Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J].Physics Letters A,1996,216(1):67-75.
[6]李向正,张卫国,原三领.LS解法和Fisher方程行波系统的定性分析[J].物理学报,2010,59(2):744-749.
[7]LI X,WANG M.A sub-ODE method for finding exact solutions of a generalized Kd V–m Kd V equation with high-order nonlinear terms[J].Physics Letters A,2007,361(1):115-118.
[8]李向正.Lax形式的5阶Kd V方程的两类尖孤立波解[J].应用数学,2014,3:008.