  We analyze topological solitons in the noncommutative plane by taking a
concrete instance of the quantum Hall system with the SU(N) symmetry, where a
soliton is identified with a skyrmion. It is shown that a topological soliton
induces an excitation of the electron number density from the ground-state
value around it. When a judicious choice of the topological charge density
$J_{0}(\mathbf{x})$ is made, it acquires a physical reality as the electron
density excitation $\Delta \rho ^{\text{cl}}(\mathbf{x})$ around a topological
soliton, $\Delta \rho ^{\text{cl}}(\mathbf{x})=-J_{0}(% \mathbf{x})$. Hence a
noncommutative soliton carries necessarily the electric charge proportional to
its topological charge. A field-theoretical state is constructed for a soliton
state irrespectively of the Hamiltonian. In general it involves an infinitely
many parameters. They are fixed by minimizing its energy once the Hamiltonian
is chosen. We study explicitly the cases where the system is governed by the
hard-core interaction and by the noncommutative CP$^{N-1}$ model, where all
these parameters are determined analytically and the soliton excitation energy
is obtained.

High Energy Physics - Theory;Mesoscale and Nanoscale Physics