The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions -- Asymptotic estimates of solutions of the Korteweg-de Vries equation on right half lines slowly moving to the left -- Multisoliton phase shifts for the korteweg-de vries equation in the case of a nonzero reflection coefficient -- On the approximation of a real potential in the Zakharov-Shabat system by its reflectionless part -- Decomposition and estimates of solutions of the modified Korteweg-de Vries equation on right half lines slowly moving leftward -- Multisoliton phase shifts for the modified Korteweg-de Vries equation in the case of a nonzero reflection coefficient -- Asymptotic estimates of solutions of the Sine-Gordon equation on right half lines almost linearly moving leftward -- On the approximation of a complex potential in the Zakharov-Shabat system by its reflectionless part