TY - BOOK ID - 7912446 TI - Algebraic approaches to partial differential equations PY - 2013 SN - 3642427626 3642368735 3642368743 PB - New York : Springer, DB - UniCat KW - Differential equations, Hyperbolic -- Numerical solutions. KW - Differential equations, Partial -- Numerical solutions. KW - Differential equations, Partial. KW - Mathematics. KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Differential equations. KW - Differential-algebraic equations. KW - Algebraic-differential equations KW - Differential-algebraic systems KW - Equations, Algebraic-differential KW - Equations, Differential-algebraic KW - Systems, Differential-algebraic KW - 517.91 Differential equations KW - Differential equations KW - Partial differential equations. KW - Applied mathematics. KW - Engineering mathematics. KW - Mathematical physics. KW - Partial Differential Equations. KW - Mathematical Physics. KW - Applications of Mathematics. KW - Differential equations, partial. KW - Partial differential equations KW - Math KW - Science KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Physical mathematics KW - Physics KW - Differential equations, Partial KW - Numerical solutions. UR - https://www.unicat.be/uniCat?func=search&query=sysid:7912446 AB - This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation,  the KP equation,  the nonlinear Schrodinger equation,  the Davey and Stewartson equations, the Boussinesq equations in geophysics,  the Navier-Stokes equations and the boundary layer problems.  In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions,  symmetry transformations,  linearization techniques  and  special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research. ER -