The fifth-order partial differential equation for the description of the Fermi-Pasta-Ulam model
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The nonlinear fifth-order PDE for the description of the Fermi–Pasta–Ulam mass chain is considered.

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The Painlevé approach is used to investigate the equation.

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It is shown that the equation does not pass the Painlevé test.

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The logistic function method is applied to obtain the travelling wave solutions.

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The pseudospectral method is used to find numerical solutions of the mathematical model.

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