Phase-Shifted Nanopteron Solutions to a Singularly Perturbed Korteweg--de Vries Equation

Timothy E. Faver

We construct nanopteron solutions to the differential equation \[ ε^2u^{(4)}+u''-u+u^2 =0, \] which is a singular perturbation of the traveling wave problem $u^{\prime \prime }-u+u^2=0$ for the K…