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arXiv · 1902.02702

Preliminary Group Classification and some exact solutions of 2Hessian equation

Mahdieh Yourdkhany·Mehdi Nadjafikhah·Megerdich Toomanian
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Abstract

We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f), with the aid of a method, then we take their projections on the space (x,y,z,f), so we prove an optimal system of one-dimensional Lie sub algebras of this equation is generated by A1 to A12, which introduced in theorem 2, ultimately, A number of new interesting nonlinear invariant models are obtained which have non-trivial in variance algebras. The result of these works is a wide class of equations which summarized in table. So at the end of this work, some exact solutions of 2-hessian equation are presented. The paper is one of the few applications of an algebraic approach to the group classification using Lie method.

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Mahdieh Yourdkhany, Mehdi Nadjafikhah, Megerdich Toomanian. 2019-02-07. Preliminary Group Classification and some exact solutions of 2Hessian equation. https://arxiv.org/abs/1902.02702

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