Generalized Burgers equations and Euler–painlevé transcendents. I

Sachdev, P. L. ; Nair, K. R. C. ; Tikekar, V. G. (1986) Generalized Burgers equations and Euler–painlevé transcendents. I Journal of Mathematical Physics , 27 (6). pp. 1506-1622. ISSN 0022-2488

Full text not available from this repository.

Official URL:

Related URL:


Initial-value problems for the generalized Burgers equation (GBE) ut+uβux+λuα=(δ/2)uxx are discussed for the single hump type of initial data-both continuous and discontinuous. The numerical solution is carried to the self-similar "intermediate asymptotic" regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painleve equations categorize the Kortweg–de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±∞, is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient λ, are also discussed. The results are compared with those holding for the modified KdV equation with damping.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:33783
Deposited On:30 Mar 2011 13:35
Last Modified:30 Mar 2011 13:35

Repository Staff Only: item control page