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

As one of the important physical models, the variable-coefficient breaking soliton model describes the dynamics of solitary waves and Riemann waves in hydrodynamics. Applying the two function approach into the variable-coefficient breaking soliton model, we find an exponential-form variable separation solution with two arbitrary functions, which covers many hyperbolic and trigonometric function solutions. Based on this solution and choosing suitably two arbitrary functions, complex waves including dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves and between dromion and periodic wave are discussed. For the complex waves such as the dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves, two components of this model possess both striking physical meanings. However, for the collision between dromion and periodic wave, one component of this model has unique physical meaning, yet the other component of the same model appears the singularity structure. Therefore, when one discusses complex waves and their collisions for one component of the model, one must take care of non-physical structures for another component of the same model lest one arbitrarily claims that he finds the so-called novel localized structures, which are actually false non-physical structures.

Complex waves and their collisions of the breaking soliton model describing hydrodynamics