Nonlinear localized waves in a medium with nonlocal interaction

V. I. Korneev^a, N. E. Kulagin^b, A. F. Popkov<sup>b

a</sup> Moscow State Institute of Electronic Technology (Technical University)
^b State Research Institute of Physical Problems

Abstract: Soliton solutions are found for nonlinear integro-differential equations with a type $\lambda/(\tau-\tau')$ 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 $\lambda$ by means of numerical calculations

Received: 10.09.1997

DOI: 10.4213/tmf846

 English version: Theoretical and Mathematical Physics, 1998, 114:3, 288–298

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