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

Authors

DOI:

https://doi.org/10.5540/tema.2019.020.03.429

Keywords:

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.

 

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Published

2019-12-02

How to Cite

Silva, Érica M., & Souza, W. L. (2019). Scaling Symmetries and Conservation Laws for Variable-coefficients Nonlinear Dispersive Equations. Trends in Computational and Applied Mathematics, 20(3), 429. https://doi.org/10.5540/tema.2019.020.03.429

Issue

Vol. 20 No. 3 (2019)

Section

Original Article

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