relativity and quantum mechanics. Noncommutative geometry is originally an interesting topic in mathematics [@1; @2; @3], In the past few years, it has been shown that some noncommutative gauge theories can be embedded in string theories [@4; @5; @6]and noncommutative geometry can also be applied to condensed matter physics. The currents and density of a system of electrons in a strong magnetic field may be described by a noncommutative quantum field theory \[7,8,9\]. The connection between a finite quantum Hall system and a noncommutative Chern-Simon Matrix model first proposed by [@hall20] was further elaborated in papers [@hall21; @hall22]. Many papers are concentrated on the research for the related questions about the quantum hall effect \[12-18\]. Since the noncommutative space resemble a quantum phase space, it exhibits an interesting spacetime uncertainty relation, which cause a $UV/IR$ mixing [@bib:uv1; @bib:uv2] and a teleological behavior. Noncommutative field theories can be regarded as highly constrained deformation of local field theory. Thus it may help us to understand non-locality at short distances in quantum gravity.

Solitons in various noncommutative theories have played a central role in understanding the physics of noncommutative theories and certain situations of string theories. The quantum Hall effect practically provides a 