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In this paper, we use new extended generalized Kudryashov and improved tan (ϑ 2) expansion approaches to investigate Kerr law nonlinearity in the extended Gerdjikov–Ivanov equation in a dense wavelength division multiplexed system. These methods rely on a traveling wave transformation and an auxiliary equation. These approaches successfully extract trigonometric, rational and hyperbolic solutions, along with some appropriate conditions imposed on parameters. To explain the dynamics of soliton profiles, a graphical description of newly discovered solutions is also presented, which exhibits distinct physical significance. The considered methods are recognized as useful and influential tools for creating solitary wave solutions to nonlinear problems in the mathematical sciences. [ABSTRACT FROM AUTHOR]

In this work, newly created soliton solutions for ion sound and Langmuir waves with an Atangana–Baleanu fractional (ABF) are given. Symbolic software is used to perform the unified solver method (USM) and Weierstrass elliptic function method (WEFM) in order to solve this model. In terms of hyperbolic functions, extended trigonometric functions, and so forth. Single-wave solutions that were entirely novel and universal were attained. The way the soliton solutions behaved in connection with the two-dimensional (2D) and three-dimensional (3D) graphics was also investigated. The dynamic investigation of the newly created soliton solutions reveals that they have several soliton forms like single-soliton, bell-shaped and mixed-form soliton profiles. This strategy is viewed as promising for handling a range of ABF evolution systems. [ABSTRACT FROM AUTHOR]

This paper tackles the recently introduced (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation (4D-BLMPE) utilized to model wave phenomena in incompressible fluid and fluid mechanics. Modified extended tanh expansion method (METEM) and the new Kudryashov scheme are implemented to produce analytical soliton solutions for the presented equation. The traveling wave transformation is constructed, and the homogeneous balance principle is utilized to apply the two proposed techniques. Furthermore, the flat-kink, smooth-kink, singular, and periodic singular solutions are successfully extracted. Some produced solutions are illustrated graphically to understand the physical meaning of the presented model. Moreover, for the first time in this study, the effect of model parameters on kink soliton dynamics is examined, and graphical representations are depicted and interpreted. [ABSTRACT FROM AUTHOR]

In this paper, the M-lump solutions, the periodic type, and cross-kink wave solutions are acquired. Here, the Hirota bilinear operator is employed. By utilizing the symbolic computation and employing the utilized method, the (3+1)-dimensional Jimbo–Miwa (JM) equation is investigated. Based on the Hirota bilinear form, the soliton solution and periodic wave solution to the mentioned equation, respectively, are obtained. We gained plenty of multiple collisions of lumps. Next, the periodic wave and cross-kink wave have greatly enriched the existing literature on the JM equation. Through the three-dimensional designs, contour design, density design, and two-dimensional design by using Maple, the physical features of these soliton solutions are explained all right. The forms of the attained solutions are one-lump, two-lumps, and three-lumps wave solutions. Then, a class of rogue waves-type solutions to the (3+1)-dimensional JM equation within the frame of the bilinear equation is found. These results can help us better understand interesting physical phenomena and mechanisms. [ABSTRACT FROM AUTHOR]

The fractional Lakshmanan–Porsezian–Daniel equation (LPD) is a significant complex model for the fractional Schrödinger family which arises in quantum physics. This paper explores new bright and kink soliton solutions of the space-time fractional LPD equation with the Kerr law of nonlinearity. By considering the conformable derivatives, the governing model is translated into integer-order differential equations with the aid of an appropriate complex traveling wave transformation. Dynamic behavior and phase portrait of traveling wave solutions are investigated. Further, various types of bright and kinked soliton solutions under definite parametric settings are discussed. Moreover, graphical representations of the obtained solution of the diverse fractional order are depicted to naturally illustrate the constructed solution. [ABSTRACT FROM AUTHOR]

The Fitzhugh–Nagumo equation is an important nonlinear reaction-diffusion equation used to model the transmission of nerve impulses. This equation is used in biology as population genetics, the Fitzhugh–Nagumo equation is also frequently used in circuit theory. In this study, we gave solutions to the fractional Fitzhugh–Nagumo (FN) equation, the fractional Newell–Whitehead–Segel (NWS) equation, and the fractional Zeldovich equation. We have obtained exact solutions within time fractional conformable derivative for these equations. [ABSTRACT FROM AUTHOR]

The model of (2 + 1)-dimensional breaking soliton equation is proposed, and the novel soliton solutions are derived by using the variable separation and extended mapping approach of Riccati equation and then, the propagation dynamics of the solutions which include multi-dromions, ring breather, fusion solitons and other multi-solitons are also constructed. Furthermore, the rich local excitations and fractal structures are investigated. The simulation results verify the proposed scheme. It can get more abundant local excitation structures than the (1 + 1)-dimensional nonlinear systems and it has potential values for certain applications in optical field. [ABSTRACT FROM AUTHOR]

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), M -shaped rational solutions, lump soliton, kink cross-rational (KCR), periodic cross-kink rational (PCKR), periodic cross-rational (PCR) solutions for the Degasperis–Procesi (DP) equation in shallow water waves through appropriate polynomial function scheme. We also compute some interactions for stated model including interaction of M -shaped soliton with one kink, interactional solution with two kinks also lump soliton with kink one and kink two solutions. Furthermore, we made suitable 3D, 2D and contour profiles via appropriate parameters. [ABSTRACT FROM AUTHOR]

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 paper, the Allen–Cahn equation with time noise is under consideration. The extended fan-sub technique is used to find the exact solutions. The solutions are successfully extracted in the form of hyperbolic, trigonometric and mixed forms of solitons. Importantly, the physical unique value problems of the solutions are discussed using the different values of parameters. The 2D, 3D, and their corresponding contour behaviors of these solutions are depicted by choosing the different values of parameters. The stability is controlled through the Borel coefficient in the noise term. [ABSTRACT FROM AUTHOR]

This paper obtains soliton solutions to Sasa–Satsuma equation, which is studied in birefringent fibers with multiplicative noise. The extended auxiliary equation approach reveals solutions in terms of Jacobi's elliptic functions from which bright, dark and singular solitons emerge when the limiting operation is applied to the modulus of ellipticity, with the limit approaching zero or unity. [ABSTRACT FROM AUTHOR]

There is no doubt that the investigation of the interaction and propagation of plasma and electromagnetic waves play an important role in understanding these phenomena. The three-dimensional Yu–Toda–Sasa–Fukuyama equation (YTSFE) is a competent mathematical model of waves in plasma, electromagnetics, or fluids. An optimal system of infinitesimal symmetries is constructed to discover extensive and astonishingly exact solutions to the YTSFE. The outstanding solutions include periodic, polynomials, fractional, logarithmic, exponential, hyperbolic, exponential integral, Airy and complex functions. These solutions are significant because they help understand how plasma and electromagnetic applications work at different boundary or initial conditions. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to implement the collective variable method to investigate the generalized complex Ginzburg–Landau equation, which characterizes the kinetics of solitons in respect of pulse parameters for fiber optics. The statistical simulations of the interacting system of ordinary differential equations that reflect all the collective variables included in the pulse ansatz have been successfully carried out using a well-known numerical methodology, the fourth-order Runge–Kutta technique. The collective variable method is employed to plot the pulse variation characteristics as a function of propagation distance. The amplitude, temporal position, width, chirp, frequency, and phase of the pulse are all depicted against the propagated coordinate, where the width, phase of soliton, amplitude, and chirp all show a strong periodicity. The numerical dynamics of solitons have also been exhibited against varying values of pulse parameters to highlight differences in collective variables. Other key bits of the current investigation are also determined. [ABSTRACT FROM AUTHOR]

In this paper, we obtain novel solutions of a coupled ϕ 4 , a coupled nonlinear Schrödinger equation and a coupled modified Korteweg de Vries equation which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic pulse solutions or the sum of either a two-kink or a kink and an antikink solution. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well. [ABSTRACT FROM AUTHOR]

This study investigates the Hamiltonian amplitude equation by using the generalized exponential rational function method. As a result, a variety of soliton solutions have been established with different wave structures such as optical exponential, dark, singular, periodic, periodic-singular, and hyperbolic solutions. 2D and 3D graphics of certain acquired solutions are drawn with the help of computer program. By picking appropriate values for the free parameters in the obtained solutions, the physical phenomena for these obtained solutions are graphically studied and depicted. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to extract the closed-form wave solutions by means of (G ′ / G) -expansion method to the DNA flow known as the Peyrard–Bishop model which describes the nonlinear interaction between neighboring displacements and hydrogen bonds. The aforementioned model is investigated for the time-fractional order and the fractional derivatives are used in the sense of conformable derivatives. The projected method provides additional generic and comprehensive wave solutions incorporated with physical parameters whose specific values reveal different shapes of the waveform such as periodic soliton, singular kink soliton, singular anti-kink soliton, and other different types of solitons. The obtained soliton solutions are novel, advanced, distinct, and relevant based on the available information in the literature which may be applied to more complex phenomena. The three-dimensional, two-dimensional, and contour plots of some of the attained results are sketched by assigning individual values of the parameters to scrutinize the dynamic behavior of the waves. [ABSTRACT FROM AUTHOR]

The integrable Lakshmanan–Porsezian–Daniel (LPD) equation originating in nonlinear fiber is studied in this work via the Riemann–Hilbert (RH) approach. First, we give the spectral analysis of the Lax pair, from which an RH problem is formulated. Afterwards, by solving the special RH problem with reflectionless under the conditions of irregularity, the formula of general N -soliton solutions can be obtained. In addition, the localized structures and dynamic behaviors of the breathers and solitons corresponding to the real part, imaginary part and modulus of the resulting solution r (x , t) are shown graphically and discussed in detail. Unlike 1- or 2-order breathers and solitons, 3-order breathers and soliton solutions rapidly collapse when they interact with each other. This phenomenon results in unbounded amplitudes which imply that higher-order solitons are not a simple nonlinear superposition of basic soliton solutions. [ABSTRACT FROM AUTHOR]

This research is about some new exact solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. Extended Sinh-Gordon equation expansion method (ShGEEM) is applied to obtain solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. The obtained results may be used in the description of the model in a fruitful way. The novel derivative operator is applied to study the aforementioned model. The achieved results are in the form of dark, bright, and combo optical solitons. The achieved solutions are also verified by using the Mathematica software. Some of the solutions are drawn in two and three dimensions so that the results can be easily discussed through them. [ABSTRACT FROM AUTHOR]

The governing equations for fluid flows, i.e. Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) model equations represent a water wave model. These model equations describe the bidirectional propagating water wave surface. In this paper, an auto-Bäcklund transformation is being generated by utilizing truncated Painlevé expansion method for the considered equation. This paper determines the new bright soliton solutions for (2 + 1) and (3 + 1) -dimensional nonlinear KP-BBM equations. The simplified version of Hirota's technique is utilized to infer new bright soliton solutions. The results are plotted graphically to understand the physical behavior of solutions. [ABSTRACT FROM AUTHOR]

This work attempts to apply the Lie symmetry approach to an updated (2+1)-dimensional KdV equation, recently updated in A.-M. Wazwaz, Nucl. Phys. B 954 (2020) 115009. The equation can be considered as one of the famous examples of the soliton equation. The infinitesimal generators for the governing equation have been found using the invariance property of Lie groups. The commutator table, adjoint table, invariant functions and one-dimensional optimal system of subalgebras are then derived using Lie point symmetries. Some group invariant solutions are derived based on various subalgebras, symmetry reductions and an optimal system. To demonstrate the physical acceptability of the results, the obtained solutions are evaluated using numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we consider (2 + 1) and (3 + 1) -dimensional Boiti–Leon–Manna–Pempinelli equations. We obtain the soliton solutions by using the new extended direct algebraic method. The resulting solutions carry a variety of new families including the singular solution of type 1 and 2, dark, dark-bright, and dark-singular soliton solution. These solutions contain trigonometric, hyperbolic, and exponential type functions. Moreover, to highlight the important features of the obtained solutions, some three-dimensional and two-dimensional diagrams of these solutions are plotted with the suitable choice of the values of the involving parameters. [ABSTRACT FROM AUTHOR]

The multiple exp-function technique, as an extension to Hirota's perturbation algorithm, is employed to find N-soliton solutions of the 3D Vakhnenko–Parkes (3D-VP) equation. This is a straightforward and effective alternative method. Consequently, one- two- and three-soliton solutions besides the front wave solutions and their wave numbers are obtained, which are completely distinct from the other published literature. 3D and density plots were investigated via the help of the Maple package program by suitably choosing the free parameters in the solutions. Further, the physical meaning for these solutions is clarified. We mention that the propagation of high-frequency waves in a relaxing medium can be investigated by discussing the dynamical behavior of the obtained solutions for the 3D-VP equation. [ABSTRACT FROM AUTHOR]

We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are motivated by the question of how these perturbations of the equation may change the stability properties of kink solutions (one-dimensional topological solitons). We prove existence of a stationary kink solution in our setting, and perform a detailed spectral analysis of the corresponding linearized operator, based on perturbing the linearized operator around the constant-coefficient kink. We derive a formula that allows us to check whether a discrete eigenvalue emerges from the essential spectrum under this perturbation. Known examples suggest that this extra eigenvalue may have an important influence on the long-time dynamics in a neighborhood of the kink. We also establish orbital stability of solitary-wave solutions in the variable-coefficient regime, despite the possible presence of negative eigenvalues in the linearization. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained. [ABSTRACT FROM AUTHOR]

In this work, we present a collective variable (CV) approach to establish dispersive solitary wave solutions for the Kaup–Newell Equation (KNE). The full CV theory has been utilized to enunciate the soliton molecules through its ground-laying parameters including the power of each pulse, phase and center-of-mass. Additionally, the dynamics of an ultra short pulse has been analyzed by using CV. This work may be utilized for various dynamics of solitons as well as the influence the amplitude, temporal position, frequency, phase and chirp on the solitons' nonlinear parameters. Moreover, the numerical simulations have been designed by means of appropriate parameter values to explain more on the obtained results. [ABSTRACT FROM AUTHOR]

In this work, the new optical soliton solutions and interaction solutions for the space-time fractional Fokas–Lenells equation with fractional M -derivatives are constructed via three mathematical analytical techniques, namely the extended SE method, unified solver method, and three-wave methods. The results have proved the efficiency of the suggested techniques for obtaining abundant optical soliton solutions to nonlinear evolution equations (NLEEs) and closed-form solutions in the forms of rational function solutions; hyperbolic and trigonometric function solutions and multi-wave interaction solutions are obtained. These techniques are more efficient, robust, and powerful mathematical tools for acquiring several optical soliton solutions for many other fractional space-time NLEEs that arise in optical physics and plasma physics. The graphical representations of the combined optical solitons are demonstrated using three- and two-dimensional graphics. [ABSTRACT FROM AUTHOR]

The Lie symmetry method is used to obtain a variety of closed-form wave solutions for the extended (3 + 1)-dimensional Jimbo–Miwa (JM) Equation, which describes certain interesting higher-dimensional waves in ocean studies, marine engineering, and other fields. By applying the Lie symmetry technique, we explicitly investigate all the possible vector fields, commutation relations of the considered vectors, and various symmetry reductions of the equation. Based on three stages of Lie symmetry reductions, the JM equation is reduced to several nonlinear ordinary differential equations (NLODEs). Consequently, abundant closed-form wave solutions are achieved, including arbitrary functional parameters. Evolutionary dynamics of some analytic wave solutions are demonstrated through three-dimensional plots based on numerical simulation. Consequently, singular soliton, kink waves, periodic oscillating wave profiles, combined singular soliton profiles, curved-shaped multiple solitons, and periodic multiple solitons with parabolic wave profiles are demonstrated by taking advantage of symbolic computation work. The obtained analytical wave solutions, which include arbitrary independent functions and other constants of the governing equation, could be used to enrich the advanced dynamical behaviors of solitary wave solutions. Furthermore, the study of conservation laws is investigated via the Ibragimov technique for Lie point symmetries. [ABSTRACT FROM AUTHOR]

Today, most of the real physical world problems can be modeled with variable-coefficient KdV–modified KdV (vcKdV–mKdV) equation. Besides, the solution methods and their reliabilities are the most important. Therefore, a high precision numerical method is always needed. In this paper, Fourier spectral method is applied to solve the space fractional generalized vcKdV–mKdV equation and the influence of fractional orders on numerical solution of the space fractional generalized vcKdV–mKdV equation is investigated. Numerical simulations in different situations of equation are conducted, including the propagation and interaction of the generalized ball-type, kink-type and periodic-depression solitons. From the numerical experiments pondered here and compared with the other methods, it is found that the numerical solutions match well with the exact solutions, which demonstrate that the Fourier spectral method is a satisfactory and efficient algorithm. [ABSTRACT FROM AUTHOR]

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations. [ABSTRACT FROM AUTHOR]

On the basis of the Hirota bilinear method, resonance Y-shaped soliton and its interaction with other localized waves of (2+1)-dimensional bidirectional Sawada–Kotera equation are derived by introducing the constraint conditions. These types of mixed soliton solutions exhibit complex interaction phenomenon between the resonance Y-shaped solitons and line waves, breather waves, and high-order lump waves. The dynamic behaviors of the interaction solutions are analyzed and illustrated. [ABSTRACT FROM AUTHOR]

The order- n periodic solutions for the (2+1)-D complex modified Korteweg–de Vries (cmKdV) equations are investigated with the aid of Darboux transformation (DT) method. By using Taylor expansion considering the limits λ 2 k − 1 → λ 0 = − a 2 + c i (k = 1 , ... , n) , order-n rational solutions are obtained, among which the order-1 and order-2 solutions are analyzed in detail. By varying different parameter l 1 , two kinds of rational solutions are deduced, namely, the line rogue wave solutions and the lump solutions. Dynamical properties of these solitons, including speed, amplitude, and extreme values, are investigated. It is shown that the line rogue wave solutions appear and disappear, while the lump solutions are localized traveling wave solutions. [ABSTRACT FROM AUTHOR]

In this study, we have taken into account the time-fractional Ostrovsky–Benjamin–Bona–Mahony equation, which is a synthesis of the time-fractional Ostrovsky equation and time-fractional Benjamin–Bona–Mahony equations and contains both mathematical and physical properties. Traveling wave solutions are produced by using the Ostrovsky–Benjamin–Bona–Mahony equation that physically sheds light on the incoming wave event on the ocean surface, using the sub-equation and Bernoulli sub-equation function methods. These solutions are presented in hyperbolic, trigonometric, singular and dark (topological) soliton types. With the help of special values given to the coefficients in the solitons obtained, it is associated with the solutions in the literature and it is observed that the solitons produced in this study are more general. Graphs representing the stationary wave at any given moment are presented. The advantages and disadvantages as well as the similarities and differences of the method are discussed in detail. Also, the behavior of the wave and its refraction according to the velocity variable, which is a physically important factor of the traveling wave solution, is analyzed and supported by simulation. [ABSTRACT FROM AUTHOR]

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods' performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order. [ABSTRACT FROM AUTHOR]

The vector Lakshmanan–Porsezian–Daniel (vLPD) equations are mainly studied in this paper. The Darboux-dressing transformation (DDT) and infinitely-many conservation laws of the vLPD equations are constructed by the Lax pair. Furthermore, one soliton and bound-state solitons solutions of the vLPD equations are obtained by the DDT method. The obtained graphs can directly reflect the dynamic behavior of the aforementioned solutions. [ABSTRACT FROM AUTHOR]

In this paper, based on the Hirota bilinear method, the high-order breathers and interaction solutions between solitons and breathers of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation are investigated. The lump and semi-rational solutions are obtained by applying the long wave limit of the N -soliton solution. Two types of semi-rational solutions are derived by choosing specific parameters, which are the mixture of the lump solution and solitons, and the mixture of the lump solution and breathers. Furthermore, the time evolution diagram illustrate the dynamic behavior of these solutions. [ABSTRACT FROM AUTHOR]

Under investigation in this paper are new novel coherent structures of two-dimensional lump-soliton for the Mel'nikov equation. The Hirota bilinear method and Kadomtsev–Petviashvili hierarchy reduction method are applied to construct a particular family of determinant semi-rational solutions exhibiting various coherent waves to the Mel'nikov equation. We first investigate some novel coherent waves, N th-order lumps first appear from the (N + 1) dark line solitons and finally disappear into those (N + 1) dark line solitons after living on the constant background for a very short period. In contrast to the usual lump, those lumps in the coherent structures of lump-soliton are not only localized in two-dimensional space and but also localized in time. [ABSTRACT FROM AUTHOR]

The Chen–Lee–Liu equation is a modified Schrödinger equation to describe a solitary wave of ultrashort pulses in optics, which lead to a discontinuous time, so a fractal modification is suggested and a fractal variational principle is established by the semi-inverse method. [ABSTRACT FROM AUTHOR]

This paper presents new optical solitons of a fractal Fokas–Lenells equation that models the dynamics of optical fibers. The Painlevé technique is employed to identify kink soliton solutions. The constraint conditions guarantee the existence of these solitons. The outcomes of this research give new solutions that are not achieved using some already defined algorithms. The derived method is efficient and its applications are promising for other nonlinear problems. The 3D graphical illustrations of obtained results are depicted for various values of the fractal parameter. [ABSTRACT FROM AUTHOR]

In this work, we demonstrate the extraction of some optical soliton solutions of the Chen–Lee–Liu equation (CLLE) with applications in optical fibers. A novel method is presented which is called the new extended direct algebraic method (EDAM). This method is based on converting the nonlinear CLLE equation into an ordinary type equation through a wave transformation. We acquire new solutions like dark, bright, combined dark-bright, combined bright-singular and periodic singular soliton solutions by using this effective technique. These acquired soliton solutions are new with some new physical properties. Some graphical representations for these solutions are provided which prove that the new method is effective and can be extended to some similar problems. [ABSTRACT FROM AUTHOR]