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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We calculate soliton solutions to the scalar field equation of motion thatarises for the 4th-order extended Lagrangian (\(\phi^{4}\) theory) in quantumfield theory using the extended hyperbolic tangent and the sine-cosine methods.Using the former technique, ten complex soliton waves are obtained; wegraphically represent three of these profiles using density plots. In thelatter case, two real soliton solutions are obtained, of which, we demonstratethe wave profile for the positive case. Using the multiplier method, wecalculate conservation laws in \((1 + 1)\)-, \((2 + 1)\)-, and \((3 +1)\)-dimensions producing three, six, and ten conservation laws respectively.Lastly, we reflect on the application of conservation laws in particle physicsand phenomenology.

Soliton Solutions and Conservation Laws for a Self-interacting Scalar Field in \(\phi^{4}\) Theory