Linearizability of the perturbed Burgers equation
Loading...
External sources
External sources
Date
Advisor
Coadvisor
Graduate program
Undergraduate course
Journal Title
Journal ISSN
Volume Title
Publisher
Type
Article
Access right
Acesso aberto
External sources
External sources
Abstract
We show in this report that the perturbed Burgers equation ut = 2uux + uxx + ε(3 α1u2ux + 3 α2uuxx + 3 α3u2 x + α4uxxx) is equivalent, through a near-identity transformation and up to O(ε), to a linearizable equation if the condition 3 α1 - 3 α3 - 3/2α2 + 3/2α4 = 0 is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. We show, furthermore, that nonlinearizable cases lead to perturbative expansions with secular-type behavior. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.
Description
Keywords
Language
English
Citation
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v. 58, n. 2 SUPPL. B, p. 2526-2530, 1998.
