The paper derives exponentially small eigenvalue formulas for dark and bright discrete solitons, showing intersite solitons are unstable and onsite bright solitons are stable, and gives a conditional counting argument for onsite dark soliton instability.
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Exponential asymptotics of dark and bright solitons in the discrete nonlinear Schr\"odinger equation
The paper derives exponentially small eigenvalue formulas for dark and bright discrete solitons, showing intersite solitons are unstable and onsite bright solitons are stable, and gives a conditional counting argument for onsite dark soliton instability.