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):$u_x=au^2+buw+cu$,\\
$w_t=u.$
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w=\varphi(x)e^{-\lambda t}+\frac 1b[\ln\varphi(x)]'_x-\frac
cb,\quad \ u=-\lambda \varphi(x)e^{-\lambda t} ,\quad \ \lambda=\frac ba,$\hfill\break
where $\varphi(x)$ is an arbitrary function.
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 23:52
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