Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations

By Raphael Cote, Yvan Martel, F. Merle. 2009

144 citations recorded by the source corpus.

Multi-soliton solutions, i.e. solutions behaving as the sum of N given solitons as $t\to +\infty$, were constructed in previous works for the L2 critical and subcritical (NLS) and (gKdV) equations. In this paper, we extend the construction of multi-soliton solutions to the L2 supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.

Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76a2882f35bb8c3ba3ca410abf772b5b9c36b76a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. F. Merle
2. Pierre Raphael
3. Yvan Martel
4. Carlos E. Kenig
5. Hatem Zaag
6. Jérémie Szeftel
7. Raphael Cote
8. Thomas Duyckaerts

In Numerical Analysis

1. Pierre Raphael
2. Yvan Martel
3. F. Merle

In Statistical and Nonlinear Physics

1. F. Merle
2. Pierre Raphael
3. Yvan Martel
4. Carlos E. Kenig
5. Hatem Zaag
6. Raphael Cote
7. Thomas Duyckaerts
8. Jérémie Szeftel

Citations in the corpus

• Blow up for the critical gKdV equation II: minimal mass dynamics (2012, methodology): “and start defocusing, and here the sharp knowledge of the speed of defocusing is fundamental for the proof. Another approach for the construction of the minimal blow up element in the continuation of [36, 25, 31, 5, 6, 7, 19, 53] would have been to take the initial data Qb(t n) at some time t n↓ 0 w”