It is shown that the Bäcklund transformation of the modified KdV equation generates a new nonlinear evolution equation of the type \(uₜ+uₓₓₓ-1/2(uₓ)³-(3/2)uₓ\{μexp(-u)+μ'exp(u)\}²{=}0\), (with µ, µ' representing arbitrary parameters) which we call "second modified KdV" equation. Exact multi-soliton solution of the equation is obtained.
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Nakamura et al. (1980) studied this question.
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