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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |