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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation, where  b ( x , t )= b  0 ( hx ,  ht ),  h ≪1, is a slowly varying, but not small, potential. We obtain an explicit description of the trajectory of the soliton parameters of scale and position on the dynamically relevant time scale, together with an estimate on the error of size  h  1/2 . In addition to the Lyapunov analysis commonly applied to these problems, we use a local virial estimate due to Martel and Merle “Asymptotic stability of solitons for subcritical gKdV equations revisited.”  Nonlinearity  18 (2005): 55–80. The results are supported by numerics. The proof does not rely on the inverse scattering machinery and is expected to carry through for the  L  2  subcritical gKdV- p  equation, 1&lt; p &lt;5.

Dynamics of KdV Solitons in the Presence of a Slowly Varying Potential