Geodesic
A (3+1)-dimensional equation admitting a Lax representation
Izvestiya. Mathematics , Tome 40 (1993) no. 1, pp. 225-233

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An equation is found that is the second in the hierarchy of higher order equations connected with Dym's equation; equations on the scattering data are introduced; its $(3+1)$-dimensional analogue is considered which admits a Lax representation with the same operator $L$ and an operator $A$ including differentiation with respect to the additional variables; the presence of a countable family of integrable discretizations of the second Korteweg–de Vries equation is demonstrated. 
@article{IM2_1993_40_1_a6,
     author = {A. S. Piskunov},
     title = {A (3+1)-dimensional equation admitting a {Lax} representation},
     journal = {Izvestiya. Mathematics },
     pages = {225--233},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_40_1_a6/}
}
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A. S. Piskunov. A (3+1)-dimensional equation admitting a Lax representation. Izvestiya. Mathematics , Tome 40 (1993) no. 1, pp. 225-233. http://geodesic.mathdoc.fr/item/IM2_1993_40_1_a6/