Darboux transformations for two dimensional elliptic affine Toda equations - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




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Abstract: The Darboux transformations for the two dimensional elliptic affine Todaequations corresponding to all seven infinite series of affine Kac-Moodyalgebras, including $A l^{1}$, $A {2l}^{2}$, $A {2l-1}^{2}$, $B l^{1}$,$C l^{1}$, $D l^{1}$ and $D {l+1}^{2}$, are presented. The Darbouxtransformation is constructed uniformly for the latter six series of equationswith suitable choice of spectral parameters and the solutions of the Lax pairsso that all the reality symmetry, cyclic symmetry and complex orthogonalsymmetry of the corresponding Lax pairs are kept invariant. The exact solutionsof all these two dimensional elliptic affine Toda equations are obtained byusing Darboux transformations.



Author: Zi-Xiang Zhou

Source: https://arxiv.org/



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