Geodesic
Description of two soliton collision for the quartic gKdV equation
Yvan Martel1 ; Frank Merle2
1 Université de Versailles St-Quentin<br/> Laboratoire de mathématiques de Versailles<br/> 78035 Versailles cedex<br/> France
2 Université de Cergy-Pontoise, IHES and CNRS<br/> Laboratoire de mathématiques<br/>95 032 Cergy-Pontoise cedex<br/>France
Annals of mathematics, Tome 174 (2011) no. 2, pp. 757-857.

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In this paper, we give the first description of the collision of two solitons for a nonintegrable equation in a special regime. We consider solutions of the quartic gKdV equation $\partial_t u + \partial_x (\partial_x^2 u + u^4)=0$, which behave as $t\to -\infty$ like \[ u(t,x)=Q_{c_1}(x -c_1 t) + Q_{c_2}(x-c_2 t) + \eta(t,x), \] where $Q_{c}(x-ct)$ is a soliton and $\|\eta(t)\|_{H^1} \ll \|Q_{c_2}\|_{H^1}\ll \|Q_{c_1}\|_{H^1}$.
DOI : 10.4007/annals.2011.174.2.2

Yvan Martel 1 ; Frank Merle 2

1 Université de Versailles St-Quentin<br/> Laboratoire de mathématiques de Versailles<br/> 78035 Versailles cedex<br/> France
2 Université de Cergy-Pontoise, IHES and CNRS<br/> Laboratoire de mathématiques<br/>95 032 Cergy-Pontoise cedex<br/>France 
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Yvan Martel; Frank Merle. Description of two soliton collision  for the quartic gKdV equation. Annals of mathematics, Tome 174 (2011) no. 2, pp. 757-857. doi : 10.4007/annals.2011.174.2.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.2.2/

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