73 research outputs found
Traveling Wavefronts of Competing Pioneer and Climax Model with Nonlocal Diffusion
We study a competing pioneer-climax species model with nonlocal diffusion. By constructing a pair of upper-lower solutions and using the iterative
technique, we establish the existence of traveling wavefronts connecting the pioneer-existence equilibrium and the coexistence equilibrium. We also discuss the asymptotic
behavior of the wave tail for the traveling wavefronts as s=x+ct→−∞
The Degasperis-Procesi equation with self-consistent sources
The Degasperis-Procesi equation with self-consistent sources(DPESCS) is
derived. The Lax representation and the conservation laws for DPESCS are
constructed. The peakon solution of DPESCS is obtained.Comment: 15 page
A new extended matrix KP hierarchy and its solutions
With the square eigenfunctions symmetry constraint, we introduce a new
extended matrix KP hierarchy and its Lax representation from the matrix KP
hierarchy by adding a new flow. The extended KP hierarchy contains two
time series and and eigenfunctions and adjoint
eigenfunctions as components. The extended matrix KP hierarchy and its
-reduction and reduction include two types of matrix KP hierarchy
with self-consistent sources and two types of (1+1)-dimensional reduced matrix
KP hierarchy with self-consistent sources. In particular, the first type and
second type of the 2+1 AKNS equation and the Davey-Stewartson equation with
self-consistent sources are deduced from the extended matrix KP hierarchy. The
generalized dressing approach for solving the extended matrix KP hierarchy is
proposed and some solutions are presented. The soliton solutions of two types
of 2+1-dimensional AKNS equation with self-consistent sources and two types of
Davey-Stewartson equation with self-consistent sources are studied.Comment: 17 page
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