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Titlebook: Algebraic Approaches to Partial Differential Equations; Xiaoping Xu Book 2013 Springer-Verlag Berlin Heidelberg 2013 Algebraic method.Asym

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发表于 2025-3-21 19:57:29 | 显示全部楼层 |阅读模式
期刊全称Algebraic Approaches to Partial Differential Equations
影响因子2023Xiaoping Xu
视频videohttp://file.papertrans.cn/153/152547/152547.mp4
发行地址Fundamental algebraic techniques of solving PDEs.Exact solutions to physical equations.Accessibility to general audience.Includes supplementary material:
图书封面Titlebook: Algebraic Approaches to Partial Differential Equations;  Xiaoping Xu Book 2013 Springer-Verlag Berlin Heidelberg 2013 Algebraic method.Asym
影响因子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.
Pindex Book 2013
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Nonlinear Scalar Equationsrespectively. The two-soliton solution is also determined via the Hirota bilinear presentation. The KP equation is an extension of the KdV equation. We use symmetry transformations to extend the solutions of the KdV equation to the more sophisticated solutions of the KP equation. Then we solve the K
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Navier–Stokes Equationsving-frame method to solve the three-dimensional Navier–Stokes equations. Seven families of unsteady rotating asymmetric solutions with various parameters are obtained. In particular, one family of solutions blows up on a moving plane, which may be used to study abrupt high-speed rotating flows. Usi
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Classical Boundary Layer Problemsent to the surface of the body. Classical unsteady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer theory of fluid dynamics. In this chapter, we introduce various schemes with multiple parameter functions to solve these equations and obtain man
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