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:4.7. Systems of Two Equations
Equation(s):$u_x=u^mf(w)$,\\
$w_t=u^kg(w)$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution for $k\neq0$ and $m\neq1$:\hfill\break
$\displaystyle u=t^{-\frac{1}{k}}V(z), \quad \ w=W(z), \quad \
z=xt^{\frac{1-m}{k}},
$\hfill\break
where $V(z)$ and $W(z)$ are described by the system of ordinary differential equations
$$
V'_{z}=V^mf(W),\quad \ (1-m)zW'_z=kV^kg(W).
$$
Remarks:Here $f(w)$ and $g(w)$ 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:Sat 22 Sep 2007 22:54
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