Geodesic
Nonlinear $\sigma$ model for the Dodd--Bullough equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 192-199

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It is shown that the Dodd–Bullough equation is related to the nonlinear two-dimensional $\rm SL(3,R)$ sigma model in which a triplet of massless fields takes values on a sphere of three-dimensional unimodular affine space in the same way that the sine-Gordon equation is related to the $S^2$ sigma model, which describes a three-component field with values on a sphere of ordinary three-dimensional Euclidean space. Equations of motion are obtained for the $\rm SL(3,R)$ sigma model. 
@article{TMF_1984_58_2_a3,
     author = {V. V. Nesterenko},
     title = {Nonlinear $\sigma$ model for the {Dodd--Bullough} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {192--199},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a3/}
}
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V. V. Nesterenko. Nonlinear $\sigma$ model for the Dodd--Bullough equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 192-199. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a3/