Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations
Rev. Mat. Iberoamericana, Tome 27 (2011) no. 1, p. 273-302 / Harvested from Project Euclid
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Multi-soliton solutions, i.e. solutions behaving as the sum of $N$ given solitons as $t \to +\infty$, were constructed for the $L^2$ critical and subcritical (NLS) and (gKdV) equations in previous works (see [Merle, F.: Construction of solutions with exactly $k$ blow-up points for the Schrödinger equation with critical nonlinearity. Comm. Math. Phys. 129 (1990), no. 2, 223-240], [Martel, Y.: Asymptotic $N$-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations. Amer. J. Math. 127 (2005), no. 5, 1103-1140] and [Martel, Y. and Merle, F.: Multi solitary waves for nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), 849-864]). In this paper, we extend the construction of multi-soliton solutions to the $L^2$ supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.
Publié le : 2011-01-15
Classification:  multi-solitons,  generalized Korteweg-de Vries equation,  nonlinear Schrödinger equation,  instability,  supercritical problem,  35Q51,  35Q53,  35Q55 
@article{1296828835,
     author = {C\^ote
, 
Rapha\"el and Martel
, 
Yvan and Merle
, 
Frank},
     title = {Construction of multi-soliton solutions for the $L^2$-supercritical
gKdV and NLS equations},
     journal = {Rev. Mat. Iberoamericana},
     volume = {27},
     number = {1},
     year = {2011},
     pages = { 273-302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1296828835}
}

Côte
, 
Raphaël; Martel
, 
Yvan; Merle
, 
Frank. Construction of multi-soliton solutions for the $L^2$-supercritical
gKdV and NLS equations. Rev. Mat. Iberoamericana, Tome 27 (2011) no. 1, pp.  273-302. http://gdmltest.u-ga.fr/item/1296828835/