Soliton interactions and conservation laws in a semi-discrete modified KdV equation

Under investigation in this paper is a semi-discrete modified KdV equation, which arises in a wide variety of fields, such as plasma physics, electromagnetic waves in ferromagnetic, antiferromagnetic or dielectric systems. With the help of the N − fold Darboux transformation and symbolic computation, the N − soliton solutions in determinant form are presented. Through the asymptotic and graphic analysis, the elastic interaction phenomena between or among two-, three- and four-soliton solutions are discussed in detail, and some important physical quantities are accurately analyzed. In addition, infinite number of conservation laws are also constructed to illustrate the integrability of the equation. The results in this paper might be helpful for understanding the propagation and interaction properties of electromagnetic waves.