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 natural and social science, many events happened at different space-timesmay be closely correlated. Two events, A (Alice) and B (Bob) are defined ascorrelated if one event is determined by another, say, $B=\hat{f} A$ forsuitable $\hat{f}$ operators. A nonlocal AB-KdV system with shifted-parity($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal witha delay) symmetry where $B=\hat{P_s}\hat{T_d} A$ is constructed directly fromthe normal KdV equation to describe two-area physical event. The exactsolutions of the AB-KdV system, including $P_s T_d$ invariant and $P_s T_d$symmetric breaking solutions are shown by different methods. The $P_s T_d$invariant solution show that the event happened at $A$ will happen also at $B$.These solutions, such as single soliton solutions, infinitely many singularsoliton solutions, soliton-cnoidal wave interaction solutions, and symmetryreduction solutions etc., show the AB-KdV system possesses rich structures.Also, a special B\"{a}cklund transformation related to residual symmetry ispresented via the localization of the residual symmetry to find interactionsolutions between the solitons and other types of the AB-KdV system.

Exact $P_s T_d$ Invariant and $P_s T_d$ Symmetric Breaking solutions, Symmetry Reductions and B\"{a}cklund Transformations For An AB-KdV System