Geodesic
Methods of geometry of differential equations in analysis of integrable models of field theory
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 57-165

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In this paper, we investigate algebraic and geometric properties of hyperbolic Toda equations $u_{xy}=\exp(Ku)$ associated with nondegenerate symmetrizable matrices $K$. A hierarchy of analogues of the potential modified Korteweg"– de Vries equation $u_t=u_{xxx}+u_x^3$ is constructed and its relationship with the hierarchy for the Korteweg– de Vries equation $T_t=T_{xxx}+TT_x$ is established. Group-theoretic structures for the dispersionless $(2+1)$-dimensional Toda equation $u_{xy}=\exp(-u_{zz})$ are obtained. Geometric properties of the multi-component nonlinear Schrödinger equation type systems $\Psi_t=\boldsymbol i\Psi_{xx}+\boldsymbol if(|\Psi|)\Psi$ (multi-soliton complexes) are described. 
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     author = {A. V. Kiselev},
     title = {Methods of geometry of differential equations in analysis of integrable models of field theory},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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A. V. Kiselev. Methods of geometry of differential equations in analysis of integrable models of field theory. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 57-165. http://geodesic.mathdoc.fr/item/FPM_2004_10_1_a6/