NEW EXACT SOLUTIONS OF SPATIALLY AND TEMPORALLY VARYING REACTION-DIFFUSION EQUATIONS
2008 ◽
Vol 06
(04)
◽
pp. 371-381
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Keyword(s):
This paper considers reaction-diffusion equations from a new point of view, by including spatiotemporal dependence in the source terms. We show for the first time that solutions are given in terms of the classical Painlevé transcendents. We consider reaction-diffusion equations with cubic and quadratic source terms. A new feature of our analysis is that the coefficient functions are also solutions of differential equations, including the Painlevé equations. Special cases arise with elliptic functions as solutions. Additional solutions given in terms of equations that are not integrable are also considered. Solutions are constructed using a Lie symmetry approach.
2022 ◽
pp. 106232
2008 ◽
Vol 46
(6)
◽
pp. 3113-3135
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Keyword(s):
1987 ◽
Vol 10
(1)
◽
pp. 163-172
1998 ◽
Vol 41
(3)
◽
pp. 333-349
◽
1997 ◽
Vol 10
(2)
◽
pp. 179-186
2011 ◽
Vol 49
(6)
◽
pp. 2256-2276
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Keyword(s):
2007 ◽
Vol 7
(1)
◽
pp. 171-189
◽
Keyword(s):