Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation

The modified Korteweg-de Vries (mKdV) typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics. (general)