Geodesic
A geometric method for solving nonlinear partial differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 209-225

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A geometric method for investigating nonlinear partial differential equations, which was proposed earlier, is developed. The method allows one to obtain both exact solutions of equations and exact solutions of initial-value and boundary-value problems. The corresponding geometric formalism is substantiated. For a nonstationary axisymmetric filter equation, an exact solution with a given boundary regime is constructed and the filter front is obtained.
Keywords: nonlinear partial differential equations, filter equation.
Mots-clés : exact solutions 
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     author = {L. I. Rubina and O. N. Ul'yanov},
     title = {A geometric method for solving nonlinear partial differential equations},
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L. I. Rubina; O. N. Ul'yanov. A geometric method for solving nonlinear partial differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 209-225. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a18/