Bifurcation analysis and new waveforms to the first fractional WBBM equation.

This research focuses on bifurcation analysis and new waveforms for the first fractional 3D Wazwaz-Benjamin-Bona-Mahony (WBBM) structure, which arises in shallow water waves. The linear stability technique is also employed to assess the stability of the mentioned model. The suggested equation's dynamical system is obtained by applying the Galilean transformation to achieve our goal. Subsequently, bifurcation, chaos, and sensitivity analysis of the mentioned model are conducted by applying the principles of the planar dynamical system. We obtain periodic, quasi-periodic, and chaotic behaviors of the mentioned model. Furthermore, we introduce and delve into diverse solitary wave solutions, encompassing bright soliton, dark soliton, kink wave, periodic waves, and anti-kink waves. These solutions are visually presented through simulations, highlighting their distinct characteristics and existence. The results highlight the effectiveness, brevity, and efficiency of the employed integration methods. They also suggest their applicability to delving into more intricate nonlinear models emerging in modern science and engineering scenarios. The novelty of this research lies in its detailed analysis of the governing model, which provides insights into its complex dynamics and varied wave structures. This study also advances the understanding of nonlinear wave properties in shallow water by combining bifurcation analysis, chaotic behavior, waveform characteristics, and stability assessments.

New wave behaviors of the Fokas-Lenells model using three integration techniques.

In this investigation, we apply the improved Kudryashov, the novel Kudryashov, and the unified methods to demonstrate new wave behaviors of the Fokas-Lenells nonlinear waveform arising in birefringent fibers. Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. These solutions encompass periodic waves with W-shaped profiles, gradually increasing amplitudes, rapidly increasing amplitudes, double-periodic waves, and breather waves with symmetrical or asymmetrical amplitudes. Singular solitons with single and multiple breather waves are also derived. Based on these findings, we can say that our implemented methods are more reliable and useful when retrieving optical soliton results for complicated nonlinear systems. Various potential features of the derived solutions are presented graphically.

Soliton solutions for the Zoomeron model applying three analytical techniques.

The Zoomeron equation is used in various categories of soliton with unique characteristics that arise in different physical phenomena, such as fluid dynamics, laser physics, and nonlinear optics. To achieve soliton solutions for the Zoomeron nonlinear structure, we apply the unified, the Kudryashov, and the improved Kudryashov techniques. We find periodic, breather, kink, anti-kink, and dark-bell soliton solutions from the derived optical soliton solutions. Bright, dark, and bright-dark breather waves are also established. Finally, some dynamic properties of the acquired findings are displayed in 3D, density, and 2D views.

Multi-soliton, breathers, lumps and interaction solution to the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation.

In this work, we consider a (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation, which has applications in processes of interaction of exponentially localized structures. Based on the bilinear formalism and with the aid of symbolic computation, we determine multi-solitons, breather solutions, lump soliton, lump-kink waves and multi lumps using various ansatze's function. We notice that multi-lumps in the form of breathers visualize as a straight line. To realize dynamics, we commit diverse graphical analysis on the presented solutions. Obtained solutions are reliable in the mathematical physics and engineering.