Second Modified KdV Equation and Its Exact Multi-Soliton Solution

It is shown that the Backlund transformation of the modified KdV equation generates a new nonlinear evolution equation of the type \(u_{t}+u_{xxx}-\frac{1}{2}(u_{x})^{3}-(3/2)u_{x}\{\mu\exp(-u)+\mu'\exp(u)\}^{2}{=}0\), (with µ, µ' representing arbitrary parameters) which we call “second modified KdV” equation. Exact multi-soliton solution of the equation is obtained.