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## Homework Statement

Consider the Kortweg-de Vires Equation in the form

$$\frac{\partial \psi}{\partial t}+\frac{\partial^3 \psi}{\partial x^3}+6\psi\frac{\partial \psi}{\partial x}=0$$

Find the relation between the coefficients ##c## and ##d## , such that the following quantity is conserved:

$$c\; \int_{-\infty}^\infty\left(\frac{\partial\psi}{\partial x}\right)^2 \mathrm{d}x+d\;\int_{-\infty}^{\infty}\psi ^3 \mathrm{d}x$$

## Homework Equations

A local conservation law is of the form ##D_t+F_x=0##.

## The Attempt at a Solution

Usually, I would try to create a local conservation law, s.t. the quantity in question is conserved. But I really don't know how to do this in the given case. Thanks!