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Vitaly Volpert, Vitali Vougalter
Existence of stationary pulses for nonlocal reaction-diffusion equations
ABSTRACT. A nonlocal reaction-diffusion equation and a system of equations from
population dynamics are considered on the whole axis. Existence of solutions in the form of stationary pulses is proved by a perturbation
method. It is based on spectral properties of the linearized operators and on the implicit function theorem.