Asymptotic Analysis of Soliton Problems : An Inverse Scattering Approach 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.