2008/01/26 by Yu. N. Kosovtsov, Kosovtsov, Yu. N.
Mathematics · Physics and Astronomy · #34A05 #34A34 #34A35 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:34A05 #msc:34A34 #msc:34A35 #nlin.SI
paper · pdf · doi:10.48550/arxiv.0801.4081
35 pages
arxiv created 2008/01/26 · openalex publication_date 2008/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is to show on examples the types of solvable PDEs and what their general solutions look like. The solving strategy, used here, as a rule is the order reduction. The order reduction method is implemented in Maple procedure, which applicable to PDEs of different order with different number of independent variables. Some of given PDEs are solved by order lifting to PDEs, which are solvable by the subsequent order reduction.