On Generalized Nonlinear Burgers＇ Equation
On Generalized Nonlinear Burgers＇ Equation
摘要
In this work, we study the similarity analysis of the generalized nonlinear Burgers＇ equation having diffusivity and viscosity as a general functions of the particle velocity. We perform the symmetry analysis and exhibit exact solutions for various forms of the diffusivity and viscosity.
参考文献18
-
1Cantwell B J. Introduction to Symmetry Analysis. Cambridge: Cambridge University Press, 2002.
-
2Doyle J, Englefield M J. Similarity solutions of a generalized Burgers' equation. IMA Journal of Applied Mathematics, 1990, 44: 145-153.
-
3Enflo B O. Saturation of a nonlinear cylindrical sound wave generated by a sinusoidal source. J Acoust Soc Amer, 1985, 77: 54-60.
-
4Mayil V B, Senthil K M. Direct similarity solutions of the Burgers' equation with variable viscosity. Indian J Pure Appl Math, 2003, 34: 1645-1669.
-
5Nimmo J J C, Crighton D G. Geometrical and diffusive effects in nonlinear acoustic propagation over long ranges. Phil Trans R Soc Lond A, 1986, 320: 1-35.
-
6Sachdev P L et al. Large-time asymptotics for periodic solutions of some generalized Burgers' equations. Stud Appl Math, 2003, 110: 181-204.
-
7Sachdev P L, Joseph K T, Mayil Vaganan B. Exact N-wave solutions of generalized Burgers' equations. Stud Appl Math, 1996, 97: 349-367.
-
8Sachdev P L, Nair K R C, Tikekar V G. Generalized Burgers' equations and Euler-Painleve transcendents I. J Math Phys, 1986, 27: 1506-1522.
-
9Sachdev P L, Nair K R C. Generalized Burgers' equations and Euler-Painleve transcendents II. J Math Phys, 1987, 28: 997-1004.
-
10Sachdev P L, Nair K R C, Tikekar V G. Generalized Burgers' equations and Euler-Painleve transcendents III. J Math Phys, 1988, 29: 2397-2400.
-
1刘希强.n维BBM方程的解[J].聊城大学学报（自然科学版）,1996,14(3):6-9.
-
2Fan Long ZHANG Li Ya FAN.On Generalized E-Monotonicity in Banach Spaces[J].Journal of Mathematical Research and Exposition,2010,30(5):903-908.
-
3HU Shuangnian,LIAN Dongyan,DIAO Tianbo,LIU Jing.Further Results on Generalized LCM Matrices[J].Wuhan University Journal of Natural Sciences,2017,22(1):1-4. 被引量：1
-
4刘辉,谢元喜.用叠加法求Burgers-KdV方程的精确解析解[J].四川师范大学学报（自然科学版）,2005,28(2):185-187. 被引量：6
-
5CAO Fei-long LIN Shao-bo ZHANG Bao-lin.On general Bernstein and Nikol’ski type inequalities[J].Applied Mathematics(A Journal of Chinese Universities),2010,25(1):35-42.
-
6万德成,韦国伟.THE STUDY OF QUASI WAVELETS BASED NUMERICAL METHOD APPLIED TO BURGERS' EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2000,21(10):1099-1110. 被引量：1
-
7李文侠,肖冬梅.A NOTE ON GENERALIZED MORAN SET[J].Acta Mathematica Scientia,1998,18(S1):88-93.
-
8赵华文,韩众.用改进的(G'/G)展开法构造PIB方程的精确行波解[J].洛阳理工学院学报（自然科学版）,2013,23(4):75-79.
-
9谢元喜.用组合法求解Burgers-KdV方程(英文)[J].西北师范大学学报（自然科学版）,2009,45(1):40-43.
-
10苏峰,赵兴球.THE HAUSDORFF DIMENSION AND MEASURE IN GENERALIZED GEOMETRIC GRAPH DIRECTED CONSTRUCTION[J].数学物理学报（A辑）,1997,17(S1):162-167.
