Geodesic
Kinks in~systems with cubic and quartic anharmonicity
Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 1, pp. 61-68

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For a classical system of interacting particles with on-site cubic or quartic anharmonicity explicit analytic solutions of the d'Alembert equation are obtained in the form of kinks in the presence of dissipation (viscous or Rayleigh) and a constant force. These kinks will be asymptotically stable in the case of quartic anharmonicity and unstable in the case cubic anharmonicity. 
@article{TMF_1988_74_1_a4,
     author = {V. N. Kashcheev},
     title = {Kinks in~systems with cubic and quartic anharmonicity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {61--68},
     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_74_1_a4/}
}
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V. N. Kashcheev. Kinks in~systems with cubic and quartic anharmonicity. Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 1, pp. 61-68. http://geodesic.mathdoc.fr/item/TMF_1988_74_1_a4/