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In this paper, the new generalized stochastic fractional potential-KdV model is investigated analytically which describes the nonlinear optical solitons and photons propagating in electric circuits and multicomponent plasmas. The governing model is transformed into a bilinear form using the Hirota bilinear method. A variety of novel waves structures are developed in the form of lump waves, collisions between lump waves and periodic waves, collisions between lump waves or single and double-kink soliton solutions, collisions between lump, periodic, single and double-kink soliton solutions. Furthermore, the ( G ′ / G 2 ) expansion method and the Adomian decomposition method are employed to construct a number of new configurations for the governing dynamical model. To validate the scientific computations, a comparison study and stability analysis are carried out efficiently. Finally, to understand the dynamical behaviour of the the nonlinear fractional model, the 3D, 2D, and contour plots have also been demonstrated with the appropriate set of parameters. Depending upon the efficiency and the validity of the applied techniques, it is established that these strategies can also be applicable to many contemporary models. [ABSTRACT FROM AUTHOR]

In this study, we solve by involving conformable fractional derivative on time-fractional perturbed nonlinear Schrödinger model which describe the behaviour of soliton transmission on fibers optical system in physics specially in transmission of data over long distances with large bandwidth. There are two modern techniques are utilized for solving the suggested model namely the Extended hyperbolic function technique and the polynomial expansion technique. These techniques give unique, robust, and powerful solutions that are useful in many research areas. We attain different types of solutions that give unique behaviour of V shaped, singular solution, and periodic soliton solutions. These solutions are play a vital role in the soliton theory along with data transmission in optical fibers. Further we also discuss the stability of obtain solutions as well as the modulation instability of the governing NLSE. To grasp and better understanding of the solution behavior we include the 3D, contour and 2D graphics. [ABSTRACT FROM AUTHOR]

The shallow water equation, which describes fluid flow below a pressure surface, is the structure that is most frequently used for displaying free surface flows. This particular kind of approach takes into consideration the impact of gravity on fluids through the inclusion of a source term proportional to the product of the water level and ground slopes. The given model is converted into a bilinear form using the Hirota bilinear method. Which refers to the development of lump waves, collisions between lump waves and periodic waves, collisions between lump waves and single- and double-kink soliton solutions, and collisions between lump, periodic, and single- and double-kink soliton solutions. Furthermore, the exp (- ϱ (ς)) approach are applied to obtain several forms of innovative combinations for the governing dynamical fractional model. In addition, it has been confirmed that the established results are stable, and it has been helpful to validate the calculations. Moreover, multiple intriguing exact solutions are utilized to illustrate the physical nature of 3D, contour, and 2D graphs. The solution yields a set of bright, dark, periodic, rational, and elliptic function solutions. [ABSTRACT FROM AUTHOR]

In optical fiber theory, the nonlinear Schrödinger equation (NLSE) is one of the most important physical models for describing the transmission of optical soliton growth. Due to the large range of possibilities for superfast signal processing and light pulses in communications, the wave propagation in nonlinear fibers is currently a topic of substantial curiosity. In this study, the third order generalized NLSE is investigated analytically by using the extended hyperbolic function technique, the improved F-expansion method, and the Adomian decomposition method, which has great importance in applied physics especially in the study optical fibers. The obtained solutions are newly made also they have the form of optical solitons, singular bell shaped, multi-bell shaped, and singular periodic solitons wave behavior and have applications in the optical fibers transmission, physics and many other scientific fields. The stability along with the modulation instability (MI) of the governing model has also been examined to validate the results. The nonlinear model properties have been illustrated using 3D, 2D, and contour plots with the appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is one of the most important physical model in optical fiber theory for explaining changes in optical soliton growth. Due to the large range of opportunities for ultrafast signal routing systems and brief pulses of light in communications, optical soliton transmission in nonlinear fibers is currently a topic of significant interest for researchers. In this article, we study the dynamics of the generalised unstable NLSE which specified the time evolution of perturbations in barely steady or unstable media. A set of efficient analytical approaches are implemented to develop various interesting travelling wave structures such as bright, dark, singular, optical, bell shaped and periodic solitons solutions. Additionally, the stability of the obtained results is validated. Finally, the modulation instability of the governing model has also been investigated to present change effects that occurs as a result of the irregular refractive indices in an optical fiber, leading to distinct behaviour patterns. The methods as reported are applicable in clarity, effectiveness, and simplicity, establishing their applicability to various sets of dynamic and static nonlinear equations concerning evolutionary phenomena in computational physics, as well as other practical domains and numerous areas of research. [ABSTRACT FROM AUTHOR]

The generalized Korteweg–de Vries–Zakharov–Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion‐acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F$$ F $$‐expansion approach and the exp(−ϕ(ζ))$$ \exp \left(-\phi \left(\zeta \right)\right) $$‐expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell‐shaped, and single bell‐shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation is one of the significant nonlinear complex models describing the optical solitons in dispersive media. In this study, the (2+1)-dimensional chiral nonlinear Schrödinger model has been investigated analytically which is of key importantance in the field of fluid sciences. A variety of exclusive travelling waveform solutions have been established for the complex dynamical model by employing a set of eminent analytical approaches namely the extended modified auxiliary equation mapping method, the improved F -expansion method, and the unified method, respectively. We obtained different forms of solitary types solutions with the help of these technique. The outcomes are a set of bell-shaped, single periodic, optical, and multi-periodic solutions. Finally, the stability of the developed results is also established to validate the computations. The study provides a very spectacular and appropriate way to put together several interesting wave demonstrations for more complex models of current era. [ABSTRACT FROM AUTHOR]

In this study, the (2+1)-dimensional generalized Hirota–Satsuma–Ito model is studied extensively to investigate wave dynamics of shallow water. A set of state of the art analytical approaches are being employed to acquire several fascinating wave structures. We have established a comparison between exact and numerical solutions to determine the absolute error. Moreover, the modulation instability as well as the stability of the solutions are adequately discussed. The 3D, contour and 2D plots are displayed for several interesting exact solutions to understand their behaviour. These strategies are demonstrated as more strong, effective, and efficient in developing various new wave structures which have numerous applications in several mathematical physics domains. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term L x t is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp (− ξ (δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model. [ABSTRACT FROM AUTHOR]