Linearizability of the perturbed Burgers equation

Autor:	José Geraldo Pereira, Roberto André Kraenkel, E. C. De Rey Neto
Přispěvatelé:	Universidade Estadual Paulista (Unesp)
Rok vydání:	1998
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical analysis FOS: Physical sciences Applied mathematics Exactly Solvable and Integrable Systems (nlin.SI) Burgers' equation Mathematics
Zdroj:	Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP
ISSN:	1095-3787 1063-651X
DOI:	10.1103/physreve.58.2526
Popis:	We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 + \alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order \epsilon, to a linearizable equation if the condition $3\alpha_1 - 3\alpha_3 - 3/2 \alpha_2 + 3/2 \alpha_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas. Comment: 10 pages, RevTeX, no figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f177c7737f507986961a3d77b7b9d3d https://doi.org/10.1103/physreve.58.2526 Zobrazit plný text záznamu