The Lotka-Volterra competition system with diffusion is considered. The Painlevé property of this system is investigated. Exact traveling wave solutions of the Lotka-Volterra competition system are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given.
In this paper we study the self-organization process of adiabatic shear bands in OFHC copper and HY-100 steel taking into account strain hardening factor. Starting from mathematical model we present new numerical approach, which is based on Courant -Isaacson -Rees scheme that allows one to simulate fully localized plastic flow. To prove accuracy and efficiency of our method we give solutions of two benchmark problems. Next we apply the proposed method to investigate such quantitative characteristics of self-organization process of ASB as average stress, temperature, localization time and distance between ASB. Then we compare the obtained results with theoretical predictions by other authors.
A system of equations for description of the predator-prey relations is considered. The model corresponds to the modified Lotka-Volterra system with logistic growth of the prey and with both predator and prey dispersing by diffusion. The Painlevé analysis of the system of equations is studied. Exact traveling wave solutions are found by means of the Q-function method.
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