Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation

Decay of Solitary Waves of Fractional Korteweg-De Vries Type Equations

“…When the non-linearity is not an algebraic function, the asymptotic behaviour can depend at the main order on the dispersion operator and on the non-linearity. For the non-local Gross-Pitaevskii equation, de Laire-López-Martínez [17] described the asymptotic behaviour of solitary waves v c depending on a convolution function in the non-linearity. The asymptotic decay of 1 − |v c | 2 can be algebraic or exponential at infinity depending of the choice of the convolution function.…”