dorsal/arxiv
View SchemaLinearizability of the Perturbed Burgers Equation
| Authors | R. A. Kraenkel, J. G. Pereira, E. C. de Rey Neto |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9703009 |
| URL | https://arxiv.org/abs/solv-int/9703009 |
| DOI | 10.1103/PhysRevE.58.2526 |
Abstract
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.
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"abstract": "We show in this letter that the perturbed Burgers equation $u_t = 2uu_x +\nu_{xx} + \\epsilon ( 3 \\alpha_1 u^2 u_x + 3\\alpha_2 uu_{xx} + 3\\alpha_3 u_x^2 +\n\\alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and\nup to order \\epsilon, to a linearizable equation if the condition $3\\alpha_1 -\n3\\alpha_3 - 3/2 \\alpha_2 + 3/2 \\alpha_4 = 0$ is satisfied. In the case this\ncondition is not fulfilled, a normal form for the equation under consideration\nis given. Then, to illustrate our results, we make a linearizability analysis\nof the equations governing the dynamics of a one-dimensional gas.",
"arxiv_id": "solv-int/9703009",
"authors": [
"R. A. Kraenkel",
"J. G. Pereira",
"E. C. de Rey Neto"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.58.2526",
"title": "Linearizability of the Perturbed Burgers Equation",
"url": "https://arxiv.org/abs/solv-int/9703009"
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