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The purpose of this study is to introduce the wave structures and dynamical features of the third-order nonlinear Schrödinger equations (TONLSE). We take the original equation and, using the traveling wave transformation, convert it into the appropriate traveling wave system, from which we create a conserved quantity known as the Hamiltonian. The Jacobian elliptic function solution (JEF), the hyperbolic function solution, and the trigonometric function solution are just a few of the optical soliton solutions to the equation that may be found using the complete discrimination system (CDS) of polynomial method (CDSPM) and also transfer the JEF into solitary wave (SW) soltions. It also includes certain dynamic results, such as bifurcation points and critical conditions for solutions, that might be utilized to explore the dynamic features of the equation employing the CDSPM. This method could also be used for qualitative analysis. The qualitative analysis is used to illustrate the equilibrium points and phase potraits of the equation. Phase portraits are visual representations used in dynamical systems to illustrate a system's behaviour through time. They can provide crucial information about a system's stability, periodic behaviour, and the presence of attractors or repellents. [ABSTRACT FROM AUTHOR]

In this work, we retrieve a series of new wave solutions of the double dispersive equation that describes the nonlinear wave propagation in the elastic inhomogeneous Murnaghan's rod by applying a novel integration norm known as the Sardar sub-equation method (SSEM). The solutions recovered by this method can be categorized as topological, non-topological, combo topological–non-topological, periodic and mixed periodic, singular and mixed singular solutions. In addition, by allotting different values to parameters, the physical movements of attained solutions are shown by plotting the 3D, 2D and contour graphs. On the basis of achieved results, we may claim that the proposed computational method is direct, dynamics, well organized, and will be useful for solving the more complicated nonlinear problems in diverse areas together with symbolic computations, especially in engineering and applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, we study chirp-free solitons (dromions) for the higher-order nonlinear Schrödinger equation (HNLSE) having non-Kerr terms with the aid of sub-ODE scheme. We find bright and singular dromion with domain walls, rational and periodic solitons, Weierstrass elliptic functions (WEFs), Jacobi elliptic solutions (JESs) and other solitary wave solutions for our governing model. The Sub-ODE scheme is very useful scheme, providing so many new solitary wave solutions especially JES and WEF solutions. We will also construct graphs of our results in different dimensions along with constraint conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study different analytical solutions for long water-wave equation (LWWE) like lump, breathers, rogue waves, periodic cross-kink, periodic wave, lump with one and two-kink, multiwave and periodic-cross lump. We compute the essential relationship between interaction between lump periodic and kink wave, periodic cross-kink and other types of exact solutions by studying the unknown nonlinear evolution equations (NLEEs) for long water wave. We show the graphical representation for our retrieve analytical solutions to observe the behavior of effective waves. [ABSTRACT FROM AUTHOR]

This paper studies the exact traveling wave solutions to the nonlinear Dullin–Gottwald–Holm model which has the application in shallow-water waves in which the fractional derivative is considered in the sense of conformable derivative. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtained using two integration norms. For this purpose G ′ / G -expansion method and reccati mapping techniques are used. The 3D plots and their corresponding contour graphs are also depicted. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This paper studies Attilio Maccari (AM) system for some new solitary wave solutions. We used sub-ODE scheme to find kink shape, bell type, Weierstrass and Jacobi elliptic, hyperbolic, periodic and other solitary wave solutions under some constraint conditions. We will also present our results graphically in distinct dimensions. [ABSTRACT FROM AUTHOR]

Topological parameters are employed to calculate the biological activity, thermodynamic properties, chemical reactivity and physical features of different structures, since various studies show a strong bond between the molecular structure and its properties [2, 4, 8, 14, 23, 25]. Therefore, helping the researchers to make up for the shortage of laboratory experiments and can provide theoretical ground for the manufacturing of diverse products. The aim of this paper is to calculate ve-version of sum-connectivity index, harmonic index, atom bond connectivity index and geometric arithmetic index of Tickysim SpiNNaker Model Sheet, by considering edge partitioning method. These can be used for better understanding of architectural techniques and innovative designs [ABSTRACT FROM AUTHOR]

Ternary alloys of Fe are very important materials having good corrosion resistance and are also famous for several high-temperature applications. The dynamical behavior of exact traveling waves for the kinetics of phase separation in Fe–Cr–X (X = Mo, Cu) ternary alloys is modelled by convective-diffusive Cahn–Hilliard (CH) equation. A variety of nonlinear dynamical exact and solitary wave structures are extracted in several forms like rational, hyperbolic, trigonometric function solutions by the utilization of a sound computational integration tool, i.e., Φ 6 -model expansion method. Besides, we also secure mixed combined solitons and singular periodic wave solutions with unknown parameters. Moreover, the constraint conditions observed during derivation lead to substantial solutions. The findings elucidate that the governing model theoretically possesses significantly rich structures of exact traveling wave solutions. Hence, our technique via fortification of symbolic computations provides an active and potent mathematical implementation for solving diverse benevolent nonlinear wave problems. [ABSTRACT FROM AUTHOR]