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This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

In this study, through the (m + 1 G ′ ) -expansion method, we extract soliton solutions to the coupled-Higgs equation. The studied nonlinear model is known to describe Higgs mechanism. The Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. The proposed method is one of the most powerful methods for constructing soliton solutions for nonlinear partial differential equations. The obtained wave solutions include exponential, hyperbolic, and distinct structures of complex function solutions. The presented results may be helpful in explaining the physical features of various nonlinear physical phenomena. In order to analyze the dynamic behavior of all obtained solutions, we plot three-dimensional and two-dimensional graphs for the obtained solutions. [ABSTRACT FROM AUTHOR]

In this work, we investigate the Fokas system which expresses the nonlinear pulse propagation in mono-mode optical fibers. We use the m + 1 G ′ -expansion scheme and the novel modified generalized exponential rational function scheme to generate soliton solutions to the proposed model. As a result, some exact solutions are constructed including hyperbolic, exponential, dark, singular, and periodic singular solutions. In order to analyze the physical behavior of the absolute, and real parts of the obtained solutions we present the 3-D surfaces, 2-D graphs, and their contour graphs. [ABSTRACT FROM AUTHOR]

In this work, the perturbed Chen-Lee-Liu equation, which describes the propagation of an optical pulse in plasma and optical fiber is studied. The (m + 1/ G )-expansion method is used for this purpose. As a result, bright-singular, dark-singular, dark and periodic optical soliton waves are constructed. Specific values for the parameters under conditions are also provided to display the pulse propagation of the found solutions. [ABSTRACT FROM AUTHOR]

In this paper, three images of nonlinearity to the fractional Lakshmanan Porsezian Daniel model in birefringent fibers are investigated. The new bright, periodic wave and singular optical soliton solutions are constructed via the (m + G′/G) expansion method, which are applicable to the dynamics within the optical fibers. All solutions are novel compared with solutions obtained via different methods. All solutions verify the conformable Lakshmanan-Porsezian-Daniel model and also, for the existence the constraint conditions are utilized. Moreover, 2D and 3D for all solutions are plotted to more understand its physical characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we study the space-time fractional perturbed nonlinear Schrödinger equation under the Kerr law nonlinearity by using the extended sinh-Gordon equation expansion method. The perturbed nonlinear Schrödinger equation is a nonlinear model which arises in nano-fibers. Some family of optical solitons and singular periodic wave solutions are successfully revealed. The parametric conditions for the existence of valid solitons are stated. Under the choice of suitable values of the parameters, the 3-dimensional and 2-dimensional graphs to some of the reported solutions are plotted. [ABSTRACT FROM AUTHOR]

This study reveals the dark, bright, combined dark–bright, singular optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. We use two integral schemes in reaching such solutions. The constraints conditions which guarantee the existence of valid solutions are stated. By choosing the suitable values of the parameters involved, we plot the 2-dimensional and 3-dimensional surfaces to some of the obtained solutions. [ABSTRACT FROM AUTHOR]

This study uses the extended sinh-Gordon equation expansion method in constructing various optical soliton solutions to the resonant nonlinear Schrödinger equation with both spatio-temporal and inter-modal dispersions. Resonant nonlinear Schrödinger equation expresses the propagation dynamics of optical solitons and Madelung fluids. Dark, bright, combined dark–bright and singular optical solitons are successfully constructed. Under the choice of suitable values of parameters, the two-dimensional, three-dimensional and the contour graphs to some of the acquired results are plotted. The reported results may be useful in explaining the physical meaning of the studied model. [ABSTRACT FROM AUTHOR]

This paper constructs dark, bright, combined dark-bright, singular, combined singular soliton optical and singular periodic solutions to the conformable space-time fractional second order nonlinear Schrödinger equation with group velocity dispersion coefficient and spatiotemporal dispersion by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid soliton solutions are given. The reported results in this study may be helpful in explaining the physical meaning of the studied model. [ABSTRACT FROM AUTHOR]

This study reveals the dark, bright, mixed dark-bright, singular and mixed singular optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schrödinger equation by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid solitons are given. Under the choice of suitable values of the parameters and the fractional values of α and β , the 2- and 3-dimensional graphs to some of the reported solutions are plotted. [ABSTRACT FROM AUTHOR]

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ -potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters. [ABSTRACT FROM AUTHOR]