Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

Carvalho, Cindy; Harley, C.

doi:10.1016/j.cnsns.2016.10.015

Cited by 1 publication

(1 citation statement)

References 24 publications

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“…Concerning classes of third-order nonlinear evolution equations, there are several works devoted to classify them as nonlinearly self-adjoint and to construct conservation laws via Ibragimov's theorem [10,11,18,19,20,21,41,42]. The relations between Ibragimov's approach and the direct method are well known [4,46,47], and the latter is also largely employed to build up conservation laws for nonlinearly self-adjoint equations [7,13,15,22,30,44].…”

Section: Introductionmentioning

confidence: 99%

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

Silva

Souza

2019

Tend. Mat. Apl. Comput.

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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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