Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method. The Cauchy problem for the Liouville equation with a small perturbation ∂ 2 t u − ∂ 2 x u + 8 exp u = εF[u], 0 < ε ≪ 1, (0.1) u| t=0 = ψ 0 (x), ∂ t u| t=0 = ψ 1 (x), x ∈ R (0.2) is considered. The problem is...

For the exactly solvable Schwinger model one interesting question is how to infer the exact solution from perturbation theory. We give a systematic procedure of deriving the exact solution from Feynman diagrams of arbitrary order for arbitrary n-point functions. As a byproduct, from perturbation theory we derive exact integral equations that the n-point functions have to obey. )permanent addres...

An approximate analytical solution of the Balitsky–Kovchegov (BK) equation using homotopy perturbation method (HPM) is suggested in this work. We carried out our work perturbative Quantum Chromodynamics (QCD) (pQCD) dipole picture deep inelastic scattering (DIS). The BK momentum space with some change variables and truncation Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel can be reduced to Fisher–...