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

In the present paper, we are concerned with the general localized solutionsfor the complex short pulse equation including soliton, breather and rogue wavesolutions. With the aid of a generalized Darboux transformation, we constructthe $N$-bright soliton solution in a compact determinant form, then the$N$-breather solution including the Akhmediev breather and a general higherorder rogue wave solution. The first- and second-order rogue wave solutions aregiven explicitly and illustrated by graphs. The asymptotic analysis isperformed rigorously for both the $N$-soliton and the $N$-breather solutions.All three forms of the localized solutions admit either smoothed-, cusped- orlooped-type ones for the CSP equation depending on the parameters. It is notedthat, due to the reciprocal (hodograph) transformation, the rogue wave solutionto the CSP equation is different from the one to the nonlinear Schr\"odinger(NLS) equation, which could be a cusponed- or a looped one.

Multi-soliton, multi-breather and higher-order rogue wave solutions to the complex short pulse equation