Publicação: Linearizability of the perturbed Burgers equation
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1998-08-01
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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.
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Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v. 58, n. 2 SUPPL. B, p. 2526-2530, 1998.
