Group classification and conservation laws for a two-dimensional generalized Kuramoto-Sivashinsky equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The two-dimensional anisotropic Kuramoto-Sivashinsky equation is a fourth-order nonlinear evolution equation in two spatial dimensions that arises in sputter erosion and epitaxial growth on vicinal surfaces. A generalization of this equation is proposed and studied via group analysis methods. The complete group classification of this generalized Kuramoto-Sivashinsky equation is carried out; it is classified according to the property of the self-adjointness and the corresponding conservation laws are established. (C) 2013 Elsevier Ltd. All rights reserved.The two-dimensional anisotropic Kuramoto-Sivashinsky equation is a fourth-order nonlinear evolution equation in two spatial dimensions that arises in sputter erosion and epitaxial growth on vicinal surfaces. A generalization of this equation is proposed a84117135FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [2011/05855-9]2011/05855-9SEM INFORMAÇÃ

Conservation laws for a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws. (C) 2012 Elsevier B.V. All rights reserved.We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws18511271135FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2011/05855-9]Government of Russian Federation [11.G34.31.0042, 220]2011/05855–9SEM INFORMAÇÃ