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In this work, various types of soliton solutions for space–time conformable version of (n+1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation were constructed via the approach of modified extended tanh. The derivatives involved were defined to reflect the sense of space–time conformable derivatives. Furthermore, with the help of a fractional wave transformation, the conformable KP equation was reduced into an ODE of a polynomial nature. Mathematica software was used to obtain a system of algebraic equations and then solved. Finally, a graphical illustration for some of the obtained results were provided to show the effect various values of order of the conformable derivative, α (alpha) as well as k, (the sum of linear terms in the equation). [ABSTRACT FROM AUTHOR]

In this research a new fractional-order derivative is defined and applied to the fractional perturbed Chen–Lee–Liu nonlinear equation. Analytical soliton solutions are obtained by the modified $ \exp (-\Omega (\xi)) $ exp ⁡ (− Ω (ξ)) -expansion function method (MEFM). Three new groups of bright soliton solutions, dark soliton solutions, periodic tan-type singular soliton solutions and rational singular soliton solutions are constructed with specific contains over the parameters of the nonlinear fractional perturbed Chen–Lee–Liu equation. Solutions are illustrated in 3D graphs, contour plots and 2D plots. Next, we compare our results with the results obtained previously for the nonlinear perturbed CCL. It is noticed that the solutions here introduced present some complex propagation features that appears for different time values in the 2D space graphs, these complex propagation phenomena are not observed in the integer-order nonlinear perturbed CCL equation or in the fractional case for other type of fractional derivatives previously introduced in the literature The fractional-order derivative here introduced will be very useful for the description of some nonlinear dissipation, nonlinear dispersion and other complex effects in optical wave phenomena. [ABSTRACT FROM AUTHOR]

The fundamental intention of this article is to find several soliton solutions to the generalized Benjamin–Bona–Mahony equation. The fractional derivatives are described in the conformable sense. These solutions are generated using the functional variable approach. Then, we acquire via this technique some distinctive solutions, such as the singular soliton, periodic soliton, bell-shaped soliton, and kink soliton solutions. The fundamental feature of the demonstrated method is that it's convenient and provides precise, effective solutions to nonlinear equations. The solutions given will offer a thorough examination of this model and any associated occurrences. [ABSTRACT FROM AUTHOR]

In this paper, we seek to find solutions of the local time fractional Telegraph equation (LTFTE) by employing the local time fractional reduced differential transform method (LTFRDTM). This method produces a numerical approximate solution having the form of an infinite series that converges to a closed form solution in many cases. We apply LTFRDTM on four different LTFTEs to examine the efficiency of the proposed method. The yielded results established the effectiveness of LTFRDTM as a reliable and solid approach for obtaining solutions of LTFTEs. The solutions coincided with the exact solution in the ordinary case when μ = 1. It also required minimal amount of computational work and saved a lot of time. [ABSTRACT FROM AUTHOR]

The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is investigated in this study. The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is an extension of Calogero–Bogoyavlenskii–Schiff equation that describes the movement of Riemann waves along y-axis while long waves moves along the x-axis. The dynamics of Riemann waves is one of the most significant applications including tsunami in rivers, internal waves in oceans and magento-sound waves in plasmas. Finding new precise solutions with the assistance of a relatively new extended G ′ G 2 -expansion approach and exp (- φ (ζ)) -expansion technique is the primary objective of this effort. The suggested techniques are important tools in the fields of mathematical physics. Successful extraction of hyperbolic, rational, and trigonometric function solutions are achieved by using the proposed analytical methods. The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is studied for the first time using extended G ′ G 2 -expansion approach and exp (- φ (ζ)) -expansion technique in this work and novel solutions are observed. 3D plots, contour plots and 2D plots are used to depict the dynamics of the extracted solutions. [ABSTRACT FROM AUTHOR]

The principal purpose of this research is to utilize the exp-function approach for achieving exact solutions of nonlinear optical fibers, including fractional order in the sense of conformable derivatives. Owing to the algorithm of symbolic computational, Some soliton solutions are obtained, including solitary soliton, singular kink-type soliton, and periodic solitons. These results are generated and developed by using the exp-function. To the greatest of our knowledge, the soliton solutions given in this study could be highly beneficial in comprehending physical phenomena. [ABSTRACT FROM AUTHOR]

This article will investigate the exact solitary wave solutions of the (3 + 1) generalized nonlinear wave equation with gas bubbles. Gas bubble-containing liquids are frequently seen in physics, engineering, science, and other fields. We explored this model using the extended auxiliary equation method. This method gives many essential solitary wave solutions, ranging from exponential to trigonometric and hyperbolic wave solutions. The investigated solutions are entirely different and new to the reported model. These demonstrated the usefulness and efficiency of the applied method for finding partial differential equations' solitary wave solutions. Additionally, utilizing Maple mathematical software in both 2D and 3D as well as the contour plots, some of the calculated solutions are plotted to comprehend the physical structures of the investigated model. [ABSTRACT FROM AUTHOR]

In this study, we dealt with the new conservation theorem and the auxiliary method. We have applied the theorem and method to (3 + 1)-dimensional modified Wazwaz–KdV equations. When we applied a new conservation theorem to given equations, the obtained conservation laws did not satisfy the divergence condition. So, we modified the obtained conservation laws. These conservation laws contain extra terms. Finally, we applied the auxiliary method to given equations. We obtained two solution families with six exact solutions. All the obtained solutions are different from each other. For a suitable value of the solutions, the 3D and 2D surfaces have been plotted by Maple. [ABSTRACT FROM AUTHOR]

This research is concerned to some modernistic wave solutions of truncated M-fractional new Hamiltonian amplitude (NHA) equation. The dealing model relates with some disabilities of wave-train. The collected solutions can be executed in exposing of this model in prominent form. The obtained results include the trigonometric, hyperbolic trigonometric and exponential functions. Verification of the results is also done by using Mathematica tool. Two techniques named modified simplest equation (MSE) and Sardar sub-equation (SSE) techniques are employed to protect the results. The achieved results are also illustrated by 3D plots for different values of truncated M-fractional parameters. The achieved results are newer than the present results of the model in the literature. The gained results can also be fruitful for the development of model in future. [ABSTRACT FROM AUTHOR]

In this paper, the full nonlinearity form of the space–time fractional Fokas–Lenells equation is scrutinized to get new analytical solutions. To achieve this, a convenient method is applied namely, a new Kudryashov method. The achieved solutions show pulse propagation in different wave patterns such as singular bell shape, peakon, singular anti-bell shape, dark, anti-bell and bright solutions. These physical characteristics are studied thoroughly by the graphical representation, which shows the fruitfulness and functionality of the proposed method. [ABSTRACT FROM AUTHOR]

In the paper, we search for some analytical solutions for a new (3 + 1)‐dimension Boiti–Leon–Manna–Pempinelli (BLMP) equation. Based on the Hirota bilinear method, bilinear neural network framework expands to more than one hidden layer to construct test functions. By using the symbolic computation software Maple, periodic‐type I, II, and III solutions of the new (3 + 1)‐dimension BLMP equation are obtained. Besides, the evolution and dynamical characteristics of these solutions derived via the appropriate real values are also exhibited. [ABSTRACT FROM AUTHOR]

In this work, a variety of optical soliton solutions are derived for a nonlinear generalized equation with variable coefficients. At first, a computational approach is used to obtain solutions for the proposed model for a particular case. After, a generalized approach is considered to obtain other type of solutions given in a more general form. From the model considered here, the classical perturbed Fokas-Lenells equation is obtained and new optical soliton solutions for this last case are presented. Finally, some conclusions are given. [ABSTRACT FROM AUTHOR]

This article examines the complex Ginzburg–Landau equation with the beta time derivative and analyze its optical solitons and other solutions in the appearance of a detuning factor in non-linear optics. The kink, bright, W-shaped bright, and dark solitons solution of this model are acquired using the modified Exp-function and Kudryshov methods. The model is examined with quadratic-cubic law, Kerr law, and parabolic laws non-linear fibers. These solitons emerge with restrictive conditions that ensure their existence are also presented. Furthermore, the obtained and precise solutions are graphically displayed, illustrating the impact of non-linearity. The various forms of solutions to the aforementioned nonlinear equation that arises in fluid dynamics and nonlinear processes are presented. [ABSTRACT FROM AUTHOR]

From point of view of two distinct various techniques accurate solutions for the thin-film ferroelectric materials equation which plays vital role in optics are implemented which represent haw utilized waves propagate through ferroelectric materials. The first one is the modified simple equation method which surrender to the balance rule and gives closed form analytical solution for all applicable problems while the second has personal profile named theas Riccati-Bernoulli Sub-ODE method which not surrender to the balance rule and has special effective properties in calculations. These methods can be used perfectly to achieve the exact solutions for different types of nonlinear problems arising in various branches of science. Via giving the appearing variables definite values, 2D and 3D- impressive graphs of some achieved solutions are drawled. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the interaction of the rational function, hyperbolic as well as exponential function for the (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation with the aid of Hirota's bilinear approach. We find several families of lump-type solutions. This method is a powerful and advantageous mathematical tool for establishing abundant lump solutions of nonlinear partial differential equations. In order to illustrate their dynamic properties, some figures are plotted with determined parameters. [ABSTRACT FROM AUTHOR]

In this survey, the ionic currents along the microtubules equation handled by applying two different techniques. It describes the ionic transport throughout the intracellular environment. This phenomenon explains the behavior of many applications in a biological nonlinear dispatch line for ionic currents. Using two different analytical techniques on this equation allows us to get new forms of analytical solitary traveling wave solutions. The obtained solutions support many researchers concerned with the discussion of the physical properties of the ionic currents along microtubules. Microtubules are one of the main components of the cytoskeleton, and function in many operations, comprehensive constitutional backing, intracellular transmit, and DNA division. The thing which makes us applies this property in many applications for this model. The earned results demonstrate that the proposed methods are significantly powerful, evangelist, relaxing, suitable, and convenient for solving many nonlinear models. [ABSTRACT FROM AUTHOR]

In this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature. [ABSTRACT FROM AUTHOR]