Geodesic
One method for solving systems of nonlinear partial differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 238-246

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A method for reducing systems of partial differential equations to corresponding systems of ordinary differential equations is proposed. We study a system of equations describing two-dimensional, cylindrical, and spherical flows of a polytropic gas, a system of dimensionless Stokes equations for the dynamics of a viscous incompressible fluid, a system of Maxwell equations for vacuum, and a system of gas dynamics equations in cylindrical coordinates. We show how this approach can be used for solving certain problems (shockless compression, turbulence, etc.).
Keywords: systems of nonlinear partial differential equations, investigation method for nonlinear partial differential equations
Mots-clés : exact solutions. 
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L. I. Rubina; O. N. Ul'yanov. One method for solving systems of nonlinear partial differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 238-246. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a22/