English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the quartic (nonintegrable) (gKdV) equation. Let u(t) be anoutgoing 2-soliton of the equation, i.e. a solution behaving exactly as the sumof two solitons (of speeds c1 and c2) for large positive time.  In arXiv:0910.3204, for nearly equal solitons, the solution u(t) is computedup to some order of epsilon=1-c2/c1, everywhere in time and space. Inparticular, it is deduced that u(t) is not a multi-soliton for large negativetime, proving the nonexistence of pure multi-soliton in this context.  In the present paper, we prove the same result for an explicit range ofspeeds: 3/4 c1< c2< c1, by a different approach, which does not longer requirea precise description of the solution. In fact, the nonexistence result holdsfor outgoing N-solitons, for any N>1, under an explicit assumption on thespeeds, which is a natural generalization of the condition for N=2.

On the nonexistence of pure multi-solitons for the quartic gKdV equation