Abstract
In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.
Highlights
It is known that these exact solutions of nonlinear evolution equations (NLEEs), especially the soliton solutions [1,2,3], can be given by using a variety of different methods [4, 5], such as Jacobi elliptic function expansion method [6], inverse scattering transformation (IST) [7, 8], Darboux transformation (DT) [9], extended generalized DT [10], Lax pair (LP) [11], Lie symmetry analysis [12], Hirota bilinear method [13], and others [14, 15]
The Hirota bilinear method is an efficient tool to construct exact solutions of NLEEs, and there exists plenty of completely integrable equations which are studied in this way
A novel method for finding the special rogue waves with predictability of NLEEs is proposed by using the Hirota bilinear method by powerful researchers in Refs. [34, 35], in which some results are very helpful for us to study some physical phenomena in engineering
Summary
It is known that these exact solutions of nonlinear evolution equations (NLEEs), especially the soliton solutions [1,2,3], can be given by using a variety of different methods [4, 5], such as Jacobi elliptic function expansion method [6], inverse scattering transformation (IST) [7, 8], Darboux transformation (DT) [9], extended generalized DT [10], Lax pair (LP) [11], Lie symmetry analysis [12], Hirota bilinear method [13], and others [14, 15]. The capable authors studied the periodic wave solutions and stability analysis for the KP-BBM equation [59] and breather and periodic wave solution for generalized Bogoyavlensky-Konopelchenko equation [60] with the aid of Hirota operator. To make this paper more self-contained, a combination of general exponential function, periodic function, and hyperbolic function of the (3 + 1)-dimensional CDG equation is constructed with the help of a bilinear operator, which is crucial to obtain the periodic-wave solution of Equation (1). Based on the Hirota bilinear form Equation (6), the general periodic-wave solution is derived in Section 2 and the novel periodic solutions which can be arisen with twenty one classes. The final section will be reserved for the conclusions and the discussions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
