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A continuum limit of the non-Hermitian spin-1/2 chain, conjectured recentlyto belong to the universality class of the noisy Burgers or, equivalently,Kardar-Parisi-Zhang equation, is obtained and analyzed. The Galilean invarianceof the Burgers equation is explicitly realized in the operator algebra. In thequasi-classical limit we find nonlinear soliton excitations exhibiting the$\omega\propto k^z$ dispersion relation with dynamical exponent $z=3/2$.Comment: 12 pages, latex, no figure

Continuum Limit, Galilean Invariance, and Solitons in the Quantum Equivalent of the Noisy Burgers Equation