Construction Solutions of PDE in Parametric Form
The new important property of wide class PDE was found solely by K. A. Volosov. We make an arbitrary replacement of variables. In the case of two independent variables 𝑥,𝑡, then it always gives the possibility of expressing all PDE second and more order as 𝐴𝑋=𝑏. This is a linear algebraic equations...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/319269 |
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| author | Alexandra K. Volosova Konstantin Alexandrovich Volosov |
| author_facet | Alexandra K. Volosova Konstantin Alexandrovich Volosov |
| author_sort | Alexandra K. Volosova |
| collection | DOAJ |
| description | The new important property of wide class PDE was found solely by K. A. Volosov. We make an arbitrary replacement of variables. In the case of two independent variables 𝑥,𝑡, then it always gives
the possibility of expressing all PDE second and more order as 𝐴𝑋=𝑏. This is a linear algebraic equations system with regards
derivatives to old variables 𝑥(𝜉,𝛿), 𝑡(𝜉,𝛿) on new variables 𝜉,𝛿∶(𝑥′𝜉,𝑥′𝛿,𝑡′𝜉,𝑡′𝛿). This
system has the unique solution. In the case of three and more independent variables
𝑥,𝑦,𝑡,…, then it gives the possibility of expressing PDE second order as
𝐴𝑋=𝑏, if we do same compliment proposes. In the present paper, we suggest a new method for constructing closed
formulas for exact solutions of PDE, then support on this important new
property. |
| format | Article |
| id | doaj-art-fb482524e53b47c3b6a5db451826e89f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fb482524e53b47c3b6a5db451826e89f2025-02-03T01:22:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/319269319269Construction Solutions of PDE in Parametric FormAlexandra K. Volosova0Konstantin Alexandrovich Volosov1Department of Applied Mathematics, Faculty of Computer Sciences, Moscow State University of Railway Engineering, 141400 Himki, Moscow region, RussiaDepartment of Applied Mathematics, Faculty of Computer Sciences, Moscow State University of Railway Engineering, 141400 Himki, Moscow region, RussiaThe new important property of wide class PDE was found solely by K. A. Volosov. We make an arbitrary replacement of variables. In the case of two independent variables 𝑥,𝑡, then it always gives the possibility of expressing all PDE second and more order as 𝐴𝑋=𝑏. This is a linear algebraic equations system with regards derivatives to old variables 𝑥(𝜉,𝛿), 𝑡(𝜉,𝛿) on new variables 𝜉,𝛿∶(𝑥′𝜉,𝑥′𝛿,𝑡′𝜉,𝑡′𝛿). This system has the unique solution. In the case of three and more independent variables 𝑥,𝑦,𝑡,…, then it gives the possibility of expressing PDE second order as 𝐴𝑋=𝑏, if we do same compliment proposes. In the present paper, we suggest a new method for constructing closed formulas for exact solutions of PDE, then support on this important new property.http://dx.doi.org/10.1155/2009/319269 |
| spellingShingle | Alexandra K. Volosova Konstantin Alexandrovich Volosov Construction Solutions of PDE in Parametric Form International Journal of Mathematics and Mathematical Sciences |
| title | Construction Solutions of PDE in Parametric Form |
| title_full | Construction Solutions of PDE in Parametric Form |
| title_fullStr | Construction Solutions of PDE in Parametric Form |
| title_full_unstemmed | Construction Solutions of PDE in Parametric Form |
| title_short | Construction Solutions of PDE in Parametric Form |
| title_sort | construction solutions of pde in parametric form |
| url | http://dx.doi.org/10.1155/2009/319269 |
| work_keys_str_mv | AT alexandrakvolosova constructionsolutionsofpdeinparametricform AT konstantinalexandrovichvolosov constructionsolutionsofpdeinparametricform |