The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can serve as the spectral parameter. 1 Formulation of the generalized chiral models Principal chiral models are important example of relativistically invariant field theory integrable by the inverse scatte...

We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the KdV equation. In this paper we: (a) Derive a Lax pair. (b) Use the Lax pair to solve the initial value problem on the line. (c) Analyze s...

For two-dimensional lattice equations one definition of integrability is that the model can be naturally and consistently extended to three dimensions, i.e., that it is “consistent around a cube” (CAC). As a consequence of CAC one can construct a Lax pair for the model. Recently Adler, Bobenko and Suris conducted a search based on this principle and certain additional assumptions. One of those ...

A systematic construction of a Lax pair and an infinite set of conservation laws for the Ernst equation is described. The matrix form of this equation is rewritten as a differential ideal of gl(2,R)-valued differential forms, and its symmetry condition is expressed as an exterior equation which is linear in the symmetry characteristic and has the form of a conservation law. By means of a recurs...

We derive the Lax connection of free fermion model on a lattice starting from fermionic formulation Bazhanov-Stroganov's three-parameter elliptic parametrization for R-operator. It results in Yang-Baxter and decorated equations difference type one spectral parameters, which is most suitable form to obtain any relativistic fermions continuous limit.

The classical Lie method is applied to a nonisospectral problem associated with system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification the symmetries provides set reductions that give rise different nontrivial spectral problems 1+1 dimensions. form which parameter Lax pair introduced carefully described.

Polynomials in differentiation operators are considered. Joint covariance with respect to Darboux transformations of a pair of such polynomials (Lax pair) as a function of one-field is studied. Methodically, the transforms of the coefficients are equalized to Frechèt differential (first term of the Taylor series on prolonged space) to establish the operator forms. In the commutative (Abelian) c...