WEAKLY NONLOCAL SOLITARY WAVES IN A SINGULARLY PERTURBED NONLINEAR SCHRODINGER-EQUATION

We consider the nonlinear Schrodinger 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 Schrodinger 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.