The superposition of algebraic solitons for the modified Korteweg–de Vries equation

• A superposition principle for the modified Korteweg–de Vries equation is studied.
• An infinite array of equally spaced, identical algebraic solitons is considered.
• The series can be summed in closed form to yield a complex valued, exact solution.

Many real nonlinear evolution equations exhibiting soliton properties display a special superposition principle, where an infinite array of equally spaced, identical solitons constitutes an exact periodic solution. This arrangement is studied for the modified Korteweg–de Vries equation with positive cubic nonlinearity, which possesses algebraic solitons with nonvanishing far field conditions. An infinite sum of equally spaced, identical algebraic pulses is evaluated in closed form, and leads to a complex valued solution of the nonlinear evolution equation.