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The Stability of Noncommutative Scalar Solitons

We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $θ$. We find an intriguing relationship between the stability and existence conditions for all level-1 solutions, in that they all have nearly-vanishing stability eigenvalues at critical $θm^2$. The stability or non-stability of the system may then be determined entirely by the $ϕ^3$ coefficient in the potential. For higher-level solutions we find an ambiguity in extrapolating solutions to finite $θ$ which prevents us from making any general statements. For these stability may be determined by comparing the fluctuation eigenvalues to critical values which we calculate.