Abstract:We consider generalizations of nonlinear Schrödinger equations, which we call Karpman equations, that include additional linear higher-order derivatives. Singularly-perturbed Karpman equations produce generalized solitary waves (GSWs) in the form of solitary waves with exponentially small oscillatory tails.Nanoptera are a special case of GSWs in which these oscillatory tails do not decay. Previous work on third-order and fourth-order Karpman equations has shown that nanoptera occur in specific continuous setti… Show more
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