Group Analysis of the Novikov Equation
Yuri Bozhkov, Igor Leite Freire, Nail H. Ibragimov
TL;DR
This paper analyzes the Novikov equation by identifying its symmetries, establishing its self-adjointness, deriving conservation laws, and exploring invariant solutions, thereby deepening understanding of its mathematical structure.
Contribution
It is the first to demonstrate the Novikov equation's strict self-adjointness and to derive associated conservation laws using symmetry analysis.
Findings
The Novikov equation is strictly self-adjoint.
A conservation law is derived from dilation symmetry.
Other symmetries do not yield nontrivial conservation laws.
Abstract
We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions.
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