Geodesic
Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 685-693

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Nonlinear wave processes described by a fifth-order generalized KdV equation derived from the Fermi–Pasta–Ulam (FPU) model are considered. It is shown that, in contrast to the KdV equation, which demonstrates the recurrence of initial states and explains the FPU paradox, the fifthorder equation fails to pass the Painlevé test, is not integrable, and does not exhibit the recurrence of the initial state. The results of this paper show that the FPU paradox occurs only at an initial stage of a numerical experiment, which is explained by the existence of KdV solitons only on a bounded initial time interval. 
@article{ZVMMF_2016_56_4_a12,
     author = {A. K. Volkov and N. A. Kudryashov},
     title = {Nonlinear waves described by a fifth-order equation derived from the {Fermi{\textendash}Pasta{\textendash}Ulam} system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {685--693},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a12/}
}
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A. K. Volkov; N. A. Kudryashov. Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 685-693. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a12/