Group-Invariant Solutions for the Generalised Fisher Type Equation

• 作者: Kirsten Louw Raseelo J. Moitsheki
• 来源期刊: 自然科学期刊(英文)
• 学科: 数学
• 关键词: SYMMETRY Methods Modified Hopf-Cole Transformation FISHER TYPE EQUATION EXACT Solutions
• 年，卷（期）: 2015,（13）
• 页码范围: 613-624
• 页数: 12页
• 分类号: O1

摘要

In this paper, we construct the group-invariant (exact) solutions for the generalised Fisher type equation using both classical Lie point and the nonclassical symmetry techniques. The generalised Fisher type equation arises in theory of population dynamics. The diffusion term and coefficient of the source term are given as the power law functions of the spatial variable. We introduce the modified Hopf-Cole transformation to simplify a nonlinear second Order Ordinary Equation (ODE) into a solvable linear third order ODE.