Study on (3+1)-dimensional nonlocal Boussinesq equation: multiple soliton solutions

What is it about?

We investigate a new (3+1)-dimensional nonlocal Boussinesq equation (nlBE). We use the Painlev\'{e} analysis to study its complete integrability in the Painlev\'{e} sense. The extended nonlocal Boussinesq system's phase shifts are investigated. Multi-soliton solutions for this system are derived using the Hirota's direct method in its streamlined form. Additionally, numerous periodic solutions, kink solutions, and singular solutions are provided. The obtained results can explain the mystery of the propagation mechanism of multiple solutions in several physical systems, including plasma physics, optical communications, oceans and seas, among others.

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