In this paper we consider the Boussinesq-Burgers equations and establish the transformation which turns the Boussinesq-Burgers equations into the single nonlinear partial differential equation, then we obtain an auto-BΓ€cklund transformation and abundant new exact solutions, including the multi-solit
Analytic multi-soliton solutions of the generalized Burgers equation
β Scribed by Jun Liu; Gui Mu; Zhengde Dai; Xi Liu
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 206 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
β¦ Synopsis
The most elementary ansatz of the double-Exp-function method for finding exact doublewave solutions can be produced by an extension of a two-soliton ansatz in a fractional form. The generalized Burgers equation is used as an example, and closed form analytic multi-soliton solutions are obtained for the first time.
π SIMILAR VOLUMES
We demonstrate that all ''new" exact solutions of the Boussinesq-Burgers equations by Rady et al. [
In this paper we study the generalized Burgers equation u t + (u 2 /2) x = f (t)u xx , where f (t) > 0 for t > 0. We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L β (R), as well it is o
A complete classification for the self-similar solutions to the generalized Burgers equation \[ u_{t}+u^{\beta} u_{x}=t^{N} u_{x x} \] of the form \(u(t, \eta)=A_{1} t^{-(1-N) / 2 \beta} F(\eta)\), where \(\eta=A_{2} x t^{-(1+N / 2}, A_{2}=1 / \sqrt{2 A}\), and \(A_{1}=\left(2 A_{2}\right)^{-1 / 6