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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):$u_x=e^{\lambda u}f(au+bw)$,\\
$w_t=e^{\beta u}g(au+bw)$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle u=U(z)-\frac{1}{\lambda}\ln{\left(x+C_1\right)}, \quad \
w=W(z)+\frac{a}{b\lambda}\ln{\left(x+C_1\right)}, \quad \
z=\frac{t+C_2}{\left(x+C_1\right)^{\beta / \lambda}},$\hfill\break
where functions $V(z)$ and $W(z)$ are described by the system of ordinary differential equations \hfill\break
$\displaystyle \beta z U'_{z}+1=-\lambda e^{\lambda U}f\left(aU+bW\right), \quad
\ W'_z=e^{\beta U}g\left(aU+bW\right).$
Remarks:Here $f(z)$ and $g(z)$ are arbitrary functions.
Novelty:Material has been fully published elsewhere
References:A.D. Polyanin, A.V. Manzhirov. Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2007, p. 1345.
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Sat 22 Sep 2007 23:24
Edits by author:0

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