Exact solutions for a forced Burgers equation with a linear external force

✍ Scribed by R.S. Zola; J.C. Dias; E.K. Lenzi; L.R. Evangelista; M.K. Lenzi; L.R. da Silva

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 308 KB
• Volume: 387
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2008.01.080

✦ Synopsis

We investigate the solutions of the Burgers equation

, where F (x, t) is an external force and Φ(x, t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F (x, t) = k 1 (t) -k 2 (t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k 1 (t) and k 2 (t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x, t) = Φ 1 (t) + Φ 2 (t)x and Φ(x, t) = Φ 3 x -Φ 4 /x 3 are incorporated in the previous analysis and exact solutions are obtained for both cases.