Gaussons: Solitons of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations

Abstract

Purpose

The purpose of this paper is to concern with a reliable treatment of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations (BEs). The author uses the sense of the Gaussian solitary waves to determine these gaussons. The study confirms that models characterized by logarithmic nonlinearity give gaussons solitons of distinct physical structures.

Design/methodology/approach

The proposed technique, as presented in this work has been shown to be very efficient for solving nonlinear equations with logarithmic nonlinearity.

Findings

The (2+1) and the (3+1)-dimensional BEs were examined as well. The examined models feature interesting results in propagation of waves and fluid flow.

Research limitations/implications

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

Practical implications

The work shows the effect of logarithmic nonlinearity compared to other nonlinearities where standard solitons appear in the last case.

Social implications

The work will benefit audience who are willing to examine the effect of logarithmic nonlinearity.

Originality/value

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

Citation

Wazwaz, A.-M. (2016), "Gaussons: Solitons of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 6, pp. 1699-1709. https://doi.org/10.1108/HFF-06-2015-0239