Abstract. We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal symmetries and formulae of nonlocal nonlinear superposition of solutions of these equations were used then for construction of chains of exact solutions. Linearization by means of the Legendre transformations of a second-order PDE with three independent variables allowed to obtain nonlocal superposition formulae for solutions of this equation, and to generate new solutions from group invariant solutions of a linear equation.
New formulae of nonlocal nonlinear superposition and generation of solutions are proposed for nonlinear diffusion-convection equations which are linearizable or are invariant with respect to a generalized hodograph transformation or connected by this transformation.We study in what particular ways additional Lie symmetries of diffusion-convection equations induce nonlocal symmetries of equations obtained from the initial ones by nonlocal transformations. The formulae derived are used for the construction of exact solutions.
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