## Abstract

We generate conservation laws for the one dimensional nonconservative Fokker-Planck (FP) equation, also known as the Kolmogorov forward equation, which describes the time evolution of the probability density function of position and velocity of a particle, and associate these, where possible, with Lie symmetry group generators. We determine the conserved vectors by a composite variational principle and then check if the condition for which symmetries associate with the conservation law is satisfied. As the Fokker-Planck equation is evolution type, no recourse to a Lagrangian formulation is made. Moreover, we obtain invariant solutions for the FP equation via potential symmetries.

Original language | English |
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Pages (from-to) | 3203-3210 |

Number of pages | 8 |

Journal | Computers and Mathematics with Applications |

Volume | 59 |

Issue number | 9 |

DOIs | |

Publication status | Published - May 2010 |

## Keywords

- Adjoint equation
- Conservation laws
- FP equation
- Lie symmetries