title: |
Rational Solutions of an Extended Lotka-Volterra Equation |
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publication: |
||
| volume-issue: | 9 - Supplement 1 | |
| pages: | 75 - 83 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2002.9.s1.7 (how to use a DOI) | |
author(s): |
X B HU, P A CLARKSON |
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publication date: |
February 2002 |
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abstract: |
A series of rational solutions are presented for an extended Lotka-Volterra eqution. These rational solutions are obtained by using Hirota's bilinear formalism and
Bäcklund transformation. The crucial step is the use of nonlinear superposition fomula.
The so-called extended Lotka-Volterra equation is [1]
d
dt
m-1
i=0
an- m-1
2
+i =
k-1
i=0
an+ m-1
2
+i-(k-1)k-1
i=0
an- m-1
2
+i (1)
(m = 1, 2, · · · ; k = 1, 2, · · · ; m = k)
or
d
dt
m-1
i=0
an- m-1
2
+i =
-k-1
i=0
an+ m+1
2
+i
-1-k-1
i=0
an- m+1
2
+i+k+1
-1
. (2)
(m = 1, 2, · · · ; -k = 1, 2, · · · )
In particular, if m = 1 in (1), equation (1) can be transformed into
d
dt
Nn =
k-1
r=1
(Nn-r - Nn+r)Nn (3)
by the variable transformation
Nn =
k-2
i=0
an+i- k
2
+1.
Copyright c 2002 by X B Hu and P A Clarkson |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |