Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form. Nonlinear equations arising from the compatibility condition of the Lax pairs in the matrix case include, in particular, Nahm equations, Volterra, Bogoyavlenskii and...

Abstract We study a Lax pair in 2-parameter Lie algebra various representations. The overlap coefficients of the eigenfunctions L and standard basis are given terms orthogonal polynomials functions. Eigenfunctions for operator $$\mathfrak {sl}(d+1,\mathbb {C})$$ sl ( d <mml:mo...

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditi...

Field equations for generalized principle models with nonconstant metric are derived and ansatz for their Lax pairs is given. Equations that define the Lax pairs are solved for the simplest solvable group. The solution is dependent on one free variable that can serve as the spectral parameter. Painlevé analysis of the resulting model is performed and its particular solutions are found 1991 MSC ...

A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A 5× 5 matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the so(p, q) Kowalewski top are found. All our Lax pairs are deformations of...