MiniLogo

EqWorld

The World of Mathematical Equations

IPM Logo

Exact Solutions Methods Software For Authors Math Forums

EqArchive: Add Equation/Solution > View Equation

 English only

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
$\displaystyle \left(\frac{\partial
w}{\partial x}\right)^2\frac{\partial^2 w}{\partial
t^2}-\left(\frac{\partial w}{\partial t}\right)^2\frac{\partial^2
w}{\partial x^2}=0$.
%where $c$ and $k$ are constants.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution:\hfill\break
$\displaystyle
w(t,x)=F\left[\frac{\left(xW-G(W)+t\right)^2}{W}\right]$,\hfill\break

where $W=W(t,x)$ is any solution of the following transcendental
equation
\hfill\break$\displaystyle G(W)-2WG\,'(W)+xW-t=0$\hfill\break
and $F(z)$ and $G(z)$ are arbitrary functions.
Novelty:Material has been fully published elsewhere
References: Yu.N. Kosovtsov. The general solutions of some nonlinear second order PDEs. I. Two independent variables, constant parameters. (2008). arXiv:0801.4081v1 [math-ph]
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Fri 08 Feb 2008 13:10
Edits by author:0

Edit (Only for author/contributor)


The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

Copyright © 2006-2011 Andrei D. Polyanin, Alexei I. Zhurov and Alexander L. Levitin