Scaling Symmetries and Conservation Laws for Variable-coefficients Nonlinear Dispersive Equations

• Autor(a) principal: SILVA,E. M.
• Data de Publicação: 2019
• Outros Autores: SOUZA,W. L.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000300429
• topic: scaling symmetries; variable-coefficients; nonlinear dispersive equations; nonlinear self-adjointness; conservation laws

Abstract: Scaling symmetries arise in different branches of physics, and symmetry-based approaches are powerful tools for studying scaling-invariant models since they can provide conservation laws that are not obvious by inspection. In this framework, the class of variable-coefficients nonlinear dispersive equations vc K ( m , n ), which contains several important evolution equations modeling nonlinear phenomena, is considered. For some of its scaling-invariant subclasses, we study its nonlinear self-adjointness and construct eight new local conservation laws associated with scaling symmetries by using a general theorem on conservation laws and the multipliers method. The property of scale invariance of those equations led to five conservation laws with a direct physical interpretation: energy, center of mass, and mass are the conserved quantities obtained in some cases.