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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.7. Systems of Two Equations
Equation(s):$u_t-u_{xx}=u(1-u^2-w^2)$,\hfill\break\quad 
$w_t-w_{xx}=-2u^2w$.
Solution(s),
Transformation(s),
Integral(s)
:
Solutions:
$$
u=\frac{a+\exp(x+t)}{a+ax-2at+\exp(x+t)},\quad
w=\pm \frac{ax-2at}{a+ax-2at+\exp(x+t)};
$$
$$
u=\frac{a+\exp(-x+t)}{a-ax-2at+\exp(-x+t)},\quad
w=\pm \frac{-ax-2at}{a-ax-2at+\exp(-x+t)},
$$
where $a$ is an arbitrary constant.
Novelty:New solution(s) / integral(s)
References:K.A. Volosov, A method of analysis for evolution systems with distributed parameters, DSc thesis, Moscow, 2007.
Author/Contributor's Details
Last name:Volosov
First name:Konstantin
Middle(s) name:Alexandrovich
Country:Russia
City:Moscow
Statistic information
Submission date:Sat 22 Sep 2007 09:04
Edits by author:0

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