Multi solitary waves for nonlinear Schrödinger equations

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Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations (2009, methodology): “In the subcritical case ([16] and [20]), one considers the sequence (un) of solutions to (gKdV) such that un(Sn) = R(Sn).”
Multi-Soliton Solutions for the Supercritical gKdV Equations (2010, background): “In fact, even for subcritical and critical cases, no general uniqueness result has been proved yet (see general existence results in [4, 14, 16, 21, 22]).”
Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension (2013, methodology): “It has already been done for the L2 critical and subcritical nonlinear Schrödinger equation (NLS) (see Merle [19] and Martel and Merle [17]), the L2 critical and subcritical generalized Korteweg–de Vries equation (gKdV) (see Martel [16]), and the L2 supercritical case both for (gKdV) and (NLS) equat”
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS (2010, methodology): “This approach is similar to the one in [24], [19], [22], [15].”
Blow up for the critical gKdV equation II: minimal mass dynamics (2012, methodology): “Another approach for the construction of the minimal blow up element in the continuation of [35, 25, 31, 5, 6, 7, 19, 52] would have been to take the initial data Qb(tn) at some time tn ↓ 0 with b(tn) = tn and to obtain uniform H1 bounds on the corresponding forward solution un(t) to (1.”