Construction Solutions of PDE in Parametric Form - Alexandra K. Volosova; Konstantin Alexandrovich Volosov (International Journal of Mathematics and Mathematical Sciences)
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.