Abstract
The nonlinear superposition formula for the Hirota lattice equation, which is equivalent to the system of nonlinear lumped self-dual network equations, was obtained. It is a recurrence relation allowing us to generate more complex soliton solutions using more simple soliton solutions. It was shown that, using the nonlinear superposition formula, one can derive breather and wobbling kink solutions. The wobbling kink solution of the Hirota lattice equation was obtained for the first time in this work.
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