Weakly Nonlocal Solitary Waves in a Singularly Perturbed Nonlinear Schrödinger Equation

We consider the nonlinear Schrödinger equation perturbed by the addition of a third-derivative term whose coefficient constitutes a small parameter. It is known from the work of Wai et al. 1] that this singular perturbation causes the solitary wave solution of the nonlinear Schrödinger equation to become nonlocal by the radiation of small-amplitude oscillatory waves. The calculation of the amplitude of these oscillatory waves requires the techniques of exponential asymptotics. This problem is re-examined here and the amplitude of the oscillatory waves calculated using the method of Borel summation. The results of Wai et al. 1] are modified and extended.