Multisoliton solutions of integrable discrete and semi-discrete principal chiral equations

- A Darboux transformation is proposed for an integrable discrete chiral equation.
- Darboux matrix is defined in terms of quasideterminant.
- Quasideterminant multisoliton solutions have been computed.
- Explicit expressions of one and two soliton solutions have been computed.

Using a quasideterminant Darboux transformation matrix, we construct soliton solutions of nonlinear integrable discrete and semi-discrete principal chiral equations (PCEs). A Darboux transformation is defined for the matrix solutions of the discrete PCE in terms of matrix solutions to the Lax pair. The solutions are expressed in terms of quasideterminants. By taking continuum limit of one independent discrete variable, we also compute quasideterminant solutions of semi-discrete PCEs. Explicit expressions of one and two soliton solutions of the discrete PCE are obtained from a seed solution by using properties of quasideterminants. It has been shown that the soliton solutions of the discrete system reduce to those of semi-discrete and usual continuum PCEs by applying appropriate limits.