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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):$u_x =aue^{\lambda w}$,\\
$w_t =bu^k.$
Solution(s),
Transformation(s),
Integral(s)
:
General solution:\hfill\break
$\displaystyle w=b\varphi(x)-\cfrac{1}{\lambda}\ln{\bigg|\psi(t)-
k\int{e^{b\lambda \varphi(x)}dx}\bigg|}, \quad\ 
u=\left[-\frac{1}{b\lambda}\frac{\psi'_{t}}{\psi(t)-
k\int{e^{b\lambda \varphi(x)}dx}}\right]^{1/k}$,\hfill\break
where $\varphi(x)$ and $\psi(t)$ are arbitrary functions.
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Sun 23 Sep 2007 00:56
Edits by author:0

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