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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:4.2. Second-Order Quasilinear Hyperbolic Equations
Equation(s):\noindent
$\displaystyle \Phi\left(t,\,\frac{\frac{\partial^2 w}{\partial t  \partial
x}}{\frac{\partial w}{\partial x}}-2bw,\,w\,\frac{\frac{\partial^2
w}{\partial t  \partial x}}{\frac{\partial w}{\partial
x}}-\frac{\partial w}{\partial t}-bw^2\right)=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution:\hfill\break
\displaystyle w(t,x)=F(t)-\frac{1}{b}\exp\left[\int
\frac{bF^2(t)+F\,'(t)+W(t)}{F(t)}\,dt \right]\left\{\int
\exp\left[\int \frac{bF^2(t)+F\,'(t)+W(t)}{F(t)}\,dt \right]
\,dt+G(x)\right\}^{-1},\hfill\break

where $W(t)$ is any solution of the following transcendental
equation
\hfill\break
$\displaystyle\Phi\left(t,\frac{-bF^2(t)+F\,'(t)+W(t)}{F(t)},W(t)\right)=0$\hfill\break
and $F(t)$ and $G(x)$ are arbitrary functions.
Remarks:Here $\Phi(t,\alpha,\beta)$ is an arbitrary function and 
$b\neq0$ is a constant.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Mon 25 Feb 2008 10:57
Edits by author:0

Edit (Only for author/contributor)


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