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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:4.5. Third-Order Equations
Equation(s):\noindent
$\displaystyle \frac{\partial w}{\partial t}+aw^k\frac{\partial w}{\partial x}-
b\frac{\partial^3 w}{\partial t^3}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Soliton-solution:\hfill\break
$\displaystyle w(x,t)=\left\{\frac{C_1(k+1)(k+2)}{2a}\cosh^{-2}\left[\frac{k}{2C_1\sqrt{b}}
(x-C_1t+C_2)\right]\right\}^{1/k}$,\hfill\break
where $C_1$ and $C_2$ are arbitrary constants.
Remarks:The author of this solution is {\bf W. E. Schiesser} (2003, private communication).
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Fri 08 Dec 2006 12:42
Edits by author:1
Last edit by author:Fri 08 Dec 2006 13:12

Edit (Only for author/contributor)


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