Abstract
A bilinear form of the (2+1)-dimensional nonlinear Calogero–Bogoyavlenskii–Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter. This parameter can control the direction, wave height and angle of the traveling wave. Based on the Hirota bilinear form and ansatz functions, we build many types of novel structures and manifold periodic-soliton solutions to the CBS model. In particular, we obtain entirely exciting periodic-soliton, cross-kinky-lump wave, double kinky-lump wave, periodic cross-kinky-lump wave, periodic two-solitary wave solutions as well as breather style of two-solitary wave solutions. We present their propagation features via changing the existence parametric values in graphically. In addition, we estimate a condition that the waves are propagated obliquely for η≠0 , and orthogonally for η=0.
Highlights
One of a significant nonlinear evolution equation is the Calogero–Bogoyavlenskii–Schiff (CBS) equation, which extensively used in various purposes
The CBS model is developed via dissimilar techniques (Peng, 2006; Kobayashi and Toda, 2006; Bruzon et al, 2003) and obtained its exact solutions (Li and Chen, 2004; Wang and Yang, 2012; Chen and Ma, 2018; Wazwaz, 2008) via the dint of symbolic computation
The multiplesoliton solutions of the CBS model were obtained by Wazwaz, (2008)
Summary
The nonlinear partial differential equations (NPDEs) have remained a subject of international research interest in physics, chemistry, biology and nonlinear sciences, especially, in nonlinear optics, photonics, BoseEinstein condensate, harbor and coastal designs (Bruzon et al, 2003; Peng, 2006; Kobayashi and Toda, 2006; Li and Chen, 2004; Wang and Yang, 2012; Chen and Ma, 2018; Wazwaz, 2008; Ullah et al, 2020; Roshid and Ma, 2018; Hossen et al, 2018; Ming et al, 2013; Roshid and Roshid, 2018; Khatun et al, 2020). The CBS model is developed via dissimilar techniques (Peng, 2006; Kobayashi and Toda, 2006; Bruzon et al, 2003) and obtained its exact solutions (Li and Chen, 2004; Wang and Yang, 2012; Chen and Ma, 2018; Wazwaz, 2008) via the dint of symbolic computation. Quasi-periodic wave solutions for the (2þ1)-dimensional generalized CBS equation was incorporated in literature by Wang and Yang (Wang and Yang (2012)). Chen and Ma (2018) explored lump wave solutions of the generalized CBS equation. We aim to determine a new bilinear form and determine innovative periodic-soliton solutions, periodic cross-kink wave, crossdouble kink-periodic wave, periodic two-solitary wave as well as breather style of two-solitary wave of the CBS model
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