Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations

By Yvan Martel. 2005

213 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/de2496f82debc2b7f6ad62aafa7847c946ebe422

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In Mathematical Physics

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Citations in the corpus

On collapsing ring blow up solutions to the mass supercritical NLS (2012, methodology): “We now aim at building an exact solution and use for this the Schauder type compactness argument designed in [22], [19], see also [16], [39].”
Asymptotic stability of solitons of the gKdV equations with general nonlinearity (2007, background): “2) This solution U(t) is called a multi-soliton solution (in [10], the result is proved only for the power case f(u) = up for p = 2, 3, 4, 5 but the proof is exactly the same for a general f(u) with stable solitons in the sense (5.”
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”
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, methodology): “The proof in [11] follows the strategy of Merle [16] (compactness argument) and relies on monotonicity properties developed in [13] (see also [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.”
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS (2010, methodology): “9and not exponential as in [19], [8] where a similar issue arises”