Rational Solutions of an Extended Lotka-Volterra Equation

DOI

10.2991/jnmp.2002.9.s1.7How to use a DOI?

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

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - X.B. Hu
AU  - P.A. Clarkson
PY  - 2002
DA  - 2002/02/01
TI  - Rational Solutions of an Extended Lotka-Volterra Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 75
EP  - 83
VL  - 9
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s1.7
DO  - 10.2991/jnmp.2002.9.s1.7
ID  - Hu2002
ER  -