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

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Algebraic Approaches to Partial Differential Equations978-3-642-36874-5

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Special Functionssigma function .(.) satisfies .′(.)/.(.)=.(.). We discuss these functions and their properties in this chapter to a certain depth. Finally, we present Jacobi’s elliptic functions ., and ., and we derive the nonlinear ordinary differential equations that they satisfy. These functions are also very us

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蠟燭

Nonlinear Scalar Equationsary parameter functions of . for the equation of transonic gas flows. Similar solutions are also obtained for the short-wave equation and the Khokhlov–Zabolotskaya equation in nonlinear acoustics of bounded bundles. The symmetry transformations and two new families of exact solutions with multiple p

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LCA Studies on Marine Alternative Fuelstum .-body systems in one dimension. If .=2, we find a connection between the Calogero–Sutherland model and the Gauss hypergeometric function. When .>2, we have a new class of multivariable hypergeometric functions. Finally, we use matrix differential operators and Fourier expansions to solve the Ma