AbstractWe consider the subcritical generalized Korteweg–de Vries equationut+(uxx+u4)x=0,t,x∈R. Let Rj(t,x)=Qcj(x−xj−cjt) (j=1,…,N) be N soliton solutions to this equation. Denote U(t) the KdV linear group, and let V be in an adequate weighted Sobolev space.We construct a solution u(t) to the generalized Korteweg–de Vries equation such thatlimt→∞‖u(t)−U(t)V−∑j=1NRj(t)‖H1=0
32 pages, submitted. Version préliminaire (2010-02) d'un travail publié sous forme définitive (2010-...
International audienceMulti-soliton solutions, i.e. solutions behaving as the sum of N given soliton...
Abstract. In this article we study the Cauchy problem in G2((0, T)×R) (the algebra of the generalize...
38 pages ; submitted ; v2: fonts modified. Version préliminaire (2009) d'un travail publié sous form...
AbstractWe consider the subcritical generalized Korteweg–de Vries equationut+(uxx+u4)x=0,t,x∈R. Let ...
Abstract. In this work we continue our study of the description of the soliton-like solutions of the...
ABSTRACT. – It is shown that if u is a solution of the initial value problem for the generalized Kor...
AbstractWe study the asymptotic behavior for large time of solutions to the Cauchy problem for the g...
In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for ...
We construct $N$-soliton solutions for the fractional Korteweg-de Vries (fKdV) equation $$ \partial_...
Abstract. We present a numerical study of solutions to general Korteweg-de Vries equations with crit...
AbstractWe show that the quartic generalised KdV equationut+uxxx+(u4)x=0 is globally well posed for ...
The paper deals with the singularly perturbed Korteweg-de Vries equation with variable coefficients....
We study the generalized Korteweg-de Vries (KdV) equations derivable from the Lagrangian L(l,p)=F[½ ...
AbstractThe asymptotic behavior of solutions of the generalized Korteweg-de Vries equation tt + uxxx...
32 pages, submitted. Version préliminaire (2010-02) d'un travail publié sous forme définitive (2010-...
International audienceMulti-soliton solutions, i.e. solutions behaving as the sum of N given soliton...
Abstract. In this article we study the Cauchy problem in G2((0, T)×R) (the algebra of the generalize...
38 pages ; submitted ; v2: fonts modified. Version préliminaire (2009) d'un travail publié sous form...
AbstractWe consider the subcritical generalized Korteweg–de Vries equationut+(uxx+u4)x=0,t,x∈R. Let ...
Abstract. In this work we continue our study of the description of the soliton-like solutions of the...
ABSTRACT. – It is shown that if u is a solution of the initial value problem for the generalized Kor...
AbstractWe study the asymptotic behavior for large time of solutions to the Cauchy problem for the g...
In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for ...
We construct $N$-soliton solutions for the fractional Korteweg-de Vries (fKdV) equation $$ \partial_...
Abstract. We present a numerical study of solutions to general Korteweg-de Vries equations with crit...
AbstractWe show that the quartic generalised KdV equationut+uxxx+(u4)x=0 is globally well posed for ...
The paper deals with the singularly perturbed Korteweg-de Vries equation with variable coefficients....
We study the generalized Korteweg-de Vries (KdV) equations derivable from the Lagrangian L(l,p)=F[½ ...
AbstractThe asymptotic behavior of solutions of the generalized Korteweg-de Vries equation tt + uxxx...
32 pages, submitted. Version préliminaire (2010-02) d'un travail publié sous forme définitive (2010-...
International audienceMulti-soliton solutions, i.e. solutions behaving as the sum of N given soliton...
Abstract. In this article we study the Cauchy problem in G2((0, T)×R) (the algebra of the generalize...
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