Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

Abstract

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent expansion method as an alternative technique to investigate more possible solutions.

Symmetry reductions of the ( 3 + 1 ) $(3+1)$ -dimensional modified Zakharov–Kuznetsov equation

“…One of the main functions for finding symmetry reductions is to use them to seek exact solutions. There are many effective direct methods that can be used to solve the obtained reduced equations such as the tanh method [28], the homogeneous balance method [29], the Horota bilinear method [30], the Darboux transformation method [31], and so on (see [32][33][34][35][36][37][38][39] for reference). Here, we use the traveling wave transformation to transform reduced equations (11) and (12) to ODEs for obtaining exact solutions.…”

Novel Soliton Solutions of Two-Mode Sawada-Kotera Equation and Its Applications

“…Lately, a novel family of nonlinear PDEs have been recognized in the name of "dual-mode" or "two-mode" about tem-poral and spatial derivatives. With regard to this curiosity, researchers have established some dual-mode nonlinear PDEs, namely two-mode (tm) mKdV equation [20], [21], tm KdV equation [10], [22], tm Sharma-Tasso-Olver equation [15], tm fifth order KdV (tmfKdV) equation [5], [23], two-mode Burger equation (tmBE) [24], tm Ostrovsky equation [25], tm perturbed Burger (tmPB) equation [25], tm KdV Burgers (tmKdVB) equation [26], tm Kadomtsev Petviashvili (tmKP) equation [27], [28], two-mode dispersive Fisher (tmdF) equation [29], tm Kuramoto-Sivashinsky (tmKS) equation [30], tm Boussinesq Burgers (tmBB) equation [31], two-mode coupled KdV and mKdV [32], [33], two-mode non-linear Schrödinger (tmNLS) [34], and tm Hirota Satsuma coupled KdV (tmHSKdV) [35] equations and the related dual-wave solutions are analyzed by different methods, such as Tanh expansion technique, (G /G)-expansion technique, rational sine-cosine technique, Kudryshov technique, simplified Hirota technique, tanh-coth tachnque, sech-csch technique, Fourier spectral technique, Bäcklund transformation scheme and trigonometric function technique [20]- [35]. As results, few solitons results in the form Kink, Kinks type of multiple soliton, periodic wave of singular kind, dark and bright solitons solutions have been conceded out for the aforementioned models.…”

Kink-Soliton, Singular-Kink-Soliton and Singular-Periodic Solutions for a New Two-Mode Version of the Burger-Huxley Model: Applications in Nerve Fibers and Liquid Crystals

“…In (1.3), if s = 0 and integrating the resulting equation once with respect to t, we get the standard single-mode Burger-Huxley equation (1.1). In this regard, many two-mode equations are established using Korsunsky's sense, and some solitary waves solutions are reported by different ansatze methods, see [9,10,11,12,13,14,15] and [16,17,18,19,20].…”