Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension

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The role of self-similarity in singularities of partial differential equations (2008, background): “Nevertheless, the existence of different self-similar solutions is known in a few particular cases, like the case p ≥ 7, where p is an odd integer (see [22]) or in space dimension d = 1 (see [111]).”
Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension (2013, background): “As a matter of fact, we have the following trapping result from Merle and Zaag [22] which asserts that wx will eventually converge to a nearby soliton, with a near parameter: Proposition 2.”
Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation (2008, methodology): “Using the convergence result of [19], we see that (10) holds for some d(0) ∈ (−1, 1) and θ(0) = ±1.”
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009, methodology): “See also the subcritical wave equation in dimension one where all blow-up profiles were found by Merle and Zaag [ MZ07 , MZ08] for general data (see the work of Caffarelli and Friedman for specific data [CF86]).”