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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A functional of the solution of the Kadomtsev-Petviashvili II equation mapsmulti-soliton solutions onto systems of vertices - structures that arelocalized around soliton junctions. A solution with one junction is mapped ontoa single vertex, which emulates a free, spatially extended, particle. Insolutions with several junctions, each junction is mapped onto a vertex. Movingin the x-y plane, the vertices collide, coalesce upon collision, and then splitup. When well separated, they emulate free particles. Multi-soliton solutions,whose structure does not change under space-time inversion as for infinitetimes, are mapped onto vertex systems that undergo elastic collisions.Solutions, whose structure does change, are mapped onto systems that undergoinelastic collisions. The inelastic vertex collisions generated from theinfinite family of (M,1) solutions (M external solitons, (M-2) Y-shaped solitonjunctions, M greater than 3) play a unique role: The only definition of vertexmass consistent with momentum conservation in these collisions is the spatialintegral of the vertex profile. This definition ensures, in addition, that, inthese collisions, the total mass and kinetic energy due to the motion in they-direction are conserved. In general, the kinetic energy due to the motion inthe x-direction is not conserved in these collisions.

Vertex dynamics in multi-soliton solutions of Kadomtsev-Petviashvili II equation