4
$\begingroup$

It is known that the Korteweg-de Vries equation $$u_{t}+uu_{x}+u_{xxx} = 0,$$ with $u=u(x,t)$ smooth and with period equal to $L$, has important conservation laws, namely, $$E(u)=\frac{1}{2}\int_{0}^{L} u_{x}^{2} - \frac{1}{3}u^{3}\ dx\ \ \text{and}\ \ F(u)=\frac{1}{2}\int_{0}^{L}u^{2}\ dx.$$

$E$ and $F$ are independent of the temporal variable $t$.

It is also knoun that the Degasperis-Procesi equation $$u_{t}-u_{xxt} = uu_{xxx}+3u_{x}u_{xx}-4u u_{x}$$ has a infinite number of conservation laws.

Question: Are there conservation laws for modified Degasperis-Procesi equation $$u_{t}-u_{xxt} = uu_{xxx}+3u_{x}u_{xx}-4u^{2}u_{x}\ \ ?$$

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ I think the question is not very clear as written. What are "the properties above" in your question? Could you please state them more precisely? $\endgroup$
    – Igor Khavkine
    Commented Jun 22, 2016 at 14:35
  • 1
    $\begingroup$ ... and please write the equation with $u_{xxx}$ and $=0$ ? $\endgroup$
    – Jean Duchon
    Commented Jun 22, 2016 at 15:10

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .