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Construction of multi-bubble solutions for the critical gKdV equation
Vianney Combet, Yvan Martel
We prove the existence of solutions of the mass critical generalized Korteweg-de Vries equation containing an arbitrary numbe…
Sharp asymptotics for the minimal mass blow up solution of critical gKdV equation
Vianney Combet, Yvan Martel
Let be a minimal mass blow up solution of the critical generalized KdV equation as constructed by Martel, Merle and Raphaël in arXiv:1204.4624. We prove both time and space sha…
Classification of minimal mass blow-up solutions for an critical inhomogeneous NLS
Vianney Combet, François Genoud
We establish the classification of minimal mass blow-up solutions of the critical inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^{\frac{4-2b…
Local Dynamics Near Unstable Branches of NLS Solitons
Vianney Combet, Tai-Peng Tsai, Ian Zwiers
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and stan…
Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension
Vianney Combet
For the L2 supercritical generalized Korteweg-de Vries equation, we proved in a previous article the existence and uniqueness of an N-parameter family of N-solitons. Recall that, f…
Multi-soliton solutions for the supercritical gKdV equations
Vianney Combet
For the L^2 subcritical and critical (gKdV) equations, Martel proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a s…
Construction and characterization of solutions converging to solitons for supercritical gKdV equations
Vianney Combet
We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcri…