Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution
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In the study of the formulation of Maxwellian tails the nonlinear partial differential equation∂2u/∂x ∂τ+∂u/∂x+u2=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.
KeywordsDifferential Equation Field Theory Elementary Particle Partial Differential Equation Quantum Field Theory
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