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| Geometric Properties and Exact Travelling WaveSolutions for the Generalized Burger-FisherEquation and the Sharma-Tasso-Olver Equation |
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| KeyWord:Monotonic and non-monotonic kink wave periodic wave ex-
act solution integrable system Burger-Fisher equation Sharma-Tasso-Olver
equation |
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| Abstract: |
| In this paper, a predator-prey model with ratio-dependent and
modified Leslie-Gower functional response subject to homogeneous Neumann
boundary condition is considered. First, properties of the constant positive sta-
tionary solution are shown, including the existence, nonexistence, multiplicity
and stability. In addition, a comparatively characterization of the stability is
obtained. Moreover, the existing result of global stability is improved. Finally,
properties of nonconstant positive stationary solutions are further studied. By
a priori estimate and the theory of Leray-Schauder degree, it is shown that
nonconstant positive stationary solutions may exist when the system has two
constant positive stationary solutions. |
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