Noether Symmetries and Conservations Laws For Non-critical Kohn-Laplace Equations on Three-Dimensional Heisenberg Group

TL;DR

This paper identifies Noether symmetries of non-critical semilinear Kohn-Laplace equations on the Heisenberg group and derives their associated conservation laws, linking symmetries to conserved quantities.

Contribution

It determines which Lie point symmetries are Noether symmetries for these equations and establishes their conservation laws, a novel connection in this context.

Findings

Identified Noether symmetries for the equations.

Derived conservation laws from these symmetries.

Clarified the relationship between symmetries and conserved quantities.

Abstract

We show which Lie point symmetries of non-critical semilinear Kohn-Laplace equations on the Heisenberg group $H^1$ are Noether symmetries and we establish their respectives conservations laws.