Volume 2 offers a unique blend of classical results of Sophus Lie with new, modern developments and numerous applications which span a period of more than 100 years. As a result, this reference is up to date, with the latest information on the group theoretic methods used frequently in mathematical physics and engineering. Volume 2 is divided into three parts. Part A focuses on relevant definitions, main algorithms, group classification schemes for partial differential equations, and multifaceted possibilities offered by Lie group theoretic philosophy. Part B contains the group analysis of a variety of mathematical models for diverse natural phenomena. It tabulates symmetry groups and solutions for linear equations of mathematical physics, classical field theory, viscous and non-Newtonian fluids, boundary layer problems, Earth sciences, elasticity, plasticity, plasma theory (Vlasov-Maxwell equations), and nonlinear optics and acoustics. Part C offers an English translation of Sophus Lie's fundamental paper on the group classification and invariant solutions of linear second-order equations with two independent variables. This will serve as a concise, practical guide to the group analysis of partial differential equations.PRESCRIBED PRESSURE (PRESSURE IS AN ARBITRARY ELEMENT) uux + vu N + E² = uyy, ux + vy = 0, where we set v = l, p = 1, and treat E² ... Classification Result For arbitrary E² = E²(N ) the principal Lie algebra Lg, is infinite and is spanned anbsp;...
|Title||:||CRC Handbook of Lie Group Analysis of Differential Equations|
|Author||:||Nail H. Ibragimov|
|Publisher||:||CRC Press - 1994-11-28|