Hybrid relativistic and modified Toda lattice-type system: equivalent form, N-fold Darboux transformation and analytic solutions

Studies of the lattice systems are of current interest due to their applications in relativity, optics, condensed matter physics and plasma physics. In this paper, we look into a hybrid relativistic and modified Toda lattice-type system. An equivalent form of that system is provided by virtue of certain transformations. Based on the Lax pair of that equivalent form, we construct an N-fold Darboux matrix and then derive the N-fold Darboux transformation, where N is a positive integer. Some analytic solutions are determined with the help of the associated N-fold Darboux transformation.

Automated summary

This paper examines a hybrid relativistic and modified Toda lattice-type system and provides an equivalent form using certain transformations. Based on the Lax pair of the equivalent form, an N-fold Darboux matrix is constructed and the N-fold Darboux transformation is derived, resulting in some analytic solutions.