A. I. Zemlyanukhin, A. V. Bochkarev, Yu. A. Blinkov
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Abstract
We propose a procedure for constructing exact solutions of equations of nonlinear mathematical physics based on the application of the Shanks extrapolation method to a segment of a perturbation series in powers of exponents that are solutions of a sequence of linear problems. We assume that a sequence of partial sums of the power series belongs to the Shanks transformation kernel. In the Shanks method, the initial value of the order of the linear combination is chosen to be one greater than the order of the pole of the solution to the original equation. The efficiency of the method is demonstrated in the construction of exact localized solutions of a nonlinear heterogeneous ordinary differential equation, the generalized Tzitzéica equation, as well as its difference and differential–difference analogues.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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