Invariant solutions and conservation laws to nonconservative FP equation

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.