Piecewise-linear soliton equations and piecewise-linear integrable maps (Q2716915)

The authors study the discrete modified Korteweg-de Vries equation NEWLINE\[NEWLINEv(x,y+1)= v(x+1,y){v(x+1,y+1) +gtv(x,y)\over tv(x+1,y+1) +fv(x,y)} \quad(f+1=1+gt),NEWLINE\]NEWLINE where \(f,g,t\) are nonnegative parameters and the independent variables \(x,y\) are assumed to be continuous variables that can take any real values (i.e., not restricted to integers). The associated (so-called piecewise linear) kink solutions and integrable maps are thoroughly discussed.