Nonlinear localized waves in a medium with nonlocal interaction

Soliton solutions are found for nonlinear integro-differential equations with a type λ/(τ-τ′) kernel used to describe particle tunneling and magnetic and superconducting vortices in a medium with nonlocal interaction. The Fourier transform method is applied to derive asymptotic formulas for even and odd localized solutions. Analytical solutions are found for particular parameter values. A complete pattern is constructed for the behavior of soliton solutions in an arbitrary range of the interaction parameter λ by means of numerical calculations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 366–379, March, 1998.