Gaussons

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.

Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple soliton solutions and a class of lump solutions

“…Following the analysis presented in Mihalache (2017) and Wazwaz (2016Wazwaz ( , 2017Wazwaz ( , 2018Wazwaz ( , 2020Wazwaz ( , 2021aWazwaz ( , 2021bWazwaz ( , 2022aWazwaz ( , 2022b, we obtain a characteristic equation with one branch for resonances at k = -1, 1, 4, 5 and 6. This branch of resonances is the same for the (2 þ 1)dimensional forms studied in Lü et al (2021), Zhou and Liu (2015) and Zhou and Zhu (2014).…”

“…To study the integrability of equation ( 4), we follow the Painlev e analysis method presented in Weiss et al (1983), Mihalache (2017), Wazwaz (2016Wazwaz ( , 2017Wazwaz ( , 2018Wazwaz ( , 2020Wazwaz ( , 2021aWazwaz ( , 2021bWazwaz ( , 2022aWazwaz ( , 2022b, Zhou and Liu (2015), Zhou and Zhu (2014) and in some of the references therein. We use the Weiss-Tabor-Carnevale-Kruskal (Weiss et al, 1983) method where a Mathematica code has been developed for performing the Painlev e test.…”

“…Nonlinear equations have many significant applications, such as plasma physics, solid state physics, fiber optics, water engineering, oceanography, wave propagation, solitary waves theory, matter-wave pulses in Bose-Einstein condensates, ion-acoustic waves in plasmas, dust acoustic waves (Baldwain and Hereman, 2006;Lü et al, 2021;Clarkson and Kruskal, 1989;Guan et al, 2020;Hirota, 1971), weakly nonlinear quasi-unidirectional waves (Khalique, 2013;Khalique and Mhalanga, 2018;Khuri, 2005Khuri, , 2008Leblond and Mihalache, 2013;Li et al, 2022), shallow water waves with weakly nonlinear restoring forces and many other scientific fields (Lü et al, 2021;Mihalache, 2017;Wazwaz, 2016Wazwaz, , 2017Wazwaz, , 2018Wazwaz, , 2020Wazwaz, , 2021aWazwaz, , 2021bWazwaz, , 2022aWazwaz, , 2022bZhou and Liu, 2015;Zhou and Zhu, 2014).…”

A Hamiltonian equation produces a variety of Painlevé integrable equations: solutions of distinct physical structures

“…Multiple soliton solutions can be found in Refs. (Hirota, 1971;Khalique, 2013;Khuri, 2005;Wazwaz, 2016Wazwaz, , 2017Wazwaz, , 2019 and in some of the references therein. 7.2.1 Using the sech 2 scheme: soliton solutions.…”

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

“…It was also reported that this equation is not integrable under inverse scattering method [31,32] and till date only three polynomial conservation laws have been given [33,34]. This equation was also explored vastly in the last few decades [35][36][37][38] and higher dimensional solitons were derived [39,40]. A 2D generalization of NLS equation is DS equation which was also derived for electrostatic ion waves [41], electron acoustic wave [42], space and laboratory dusty plasma [43], and in cylindrical geometry [44].…”