# Conservation laws and symmetries of time-dependent generalized KdV equations

## TL;DR

This paper classifies conservation laws and symmetries for time-dependent generalized KdV equations, linking them to Hamiltonian structures and discussing their physical significance.

## Contribution

It provides a complete classification of low-order conservation laws and Hamiltonian symmetries for these equations, enhancing understanding of their mathematical and physical properties.

## Key findings

- Classification of low-order conservation laws achieved
- Hamiltonian symmetries systematically derived
- Physical interpretations of laws and symmetries discussed

## Abstract

A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries is derived. The physical meaning of the conservation laws and the symmetries is discussed.