Abstract
We study a generalization of the Korteweg–de Vries equation obtained from the Fermi–Pasta–Ulam problem. We get the fifth-order nonlinear evolution equation for description of perturbations in the mass chain. Using the Painlevé test, we analyze this equation and show that it does not pass the Painlevé test in the general case. However, the necessary condition for existence of the meromorphic solution is carried out and some exact solutions can be found. We present a new approach to look for traveling wave solutions of the generalization of the Korteweg–de Vries equation. Solitary wave and elliptic solutions of the equation are found and discussed, compared to the Korteweg–de Vries soliton.
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