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Our analysis describes the transition, as $x\\rightarrow-\\infty$, between the oscillatory power-like decay asymptotics for $|s_1|<1$ (Ablowitz-Segur) to the power-like growth behavior for $|s_1|=1$ (Hastings-McLeod) and from the latter to the singular oscillatory power-like growth for $|s_1|>1$ (Kapaev). 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Our analysis describes the transition, as $x\\rightarrow-\\infty$, between the oscillatory power-like decay asymptotics for $|s_1|<1$ (Ablowitz-Segur) to the power-like growth behavior for $|s_1|=1$ (Hastings-McLeod) and from the latter to the singular oscillatory power-like growth for $|s_1|>1$ (Kapaev). 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