A natural way to model dynamic systems under uncertainty is to use fuzzy initial value problems (FIVPs) and related uncertain systems. In this paper, we express the fuzzy Laplace transform and then ...some of its well-known properties are investigated. In addition, an existence theorem is given for fuzzy-valued function which possess the fuzzy Laplace transform. Consequently, we investigate the solutions of FIVPs and the solutions in state-space description of fuzzy linear continuous-time systems under generalized H-differentiability as two new applications of fuzzy Laplace transforms. Finally, some examples are given to show the efficiency of the proposed method.
The search for soliton structures plays a pivotal role in many scientific disciplines particularly in nonlinear optics. The main concern of the present paper is to explore the dynamics of soliton ...structures in a nonlinear Schrödinger (NLS) equation with the parabolic law. In this respect, the reduced form of the NLS equation is firstly extracted; then, its soliton structures are derived in the presence of spatio-temporal dispersions using the Kudryashov method. As the completion of studies, the impact of increasing and decreasing the coefficients of the parabolic law on the dynamics of soliton structures is formally addressed through representing several two- and three-dimensional figures.
The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa–Satsuma (GSS) equation describing the propagation of the femtosecond pulses in ...the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa–Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.
The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of ...symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg–Landau equation including the parabolic nonlinearity.
•A fifth-order nonlinear water wave equation is considered.•W-shaped and other solitons involving different wave structures are retrieved.•Kudryashov methods are adopted to carry out this goal.
...Investigated in the present paper is a fifth-order nonlinear evolution (FONLE) equation, known as a nonlinear water wave (NLWW) equation, with applications in the applied sciences. More precisely, a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain. The Kudryashov methods (KMs) are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W-shaped and other solitons. In the end, the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.
Fuzzy symmetric solutions of fuzzy linear systems Allahviranloo, T.; Salahshour, S.
Journal of computational and applied mathematics,
06/2011, Letnik:
235, Številka:
16
Journal Article, Conference Proceeding
Recenzirano
Odprti dostop
In this paper, we propose a simple and practical method to solve a fuzzy linear system AX̃=b̃, where X̃ and b̃ are fuzzy triangular vectors with non-zero spreads and matrix A is nonsingular with real ...coefficients. The aim of this paper is twofold. First, we obtain the crisp solution of a fuzzy linear system. To this end, we solve the 1-cut of a fuzzy linear system. Second, we allocate some unknown symmetric spreads to any rows of fuzzy linear system in 1-cut position. Thus, a fuzzy linear system in 1-cut will be transformed to a system of interval equations. The symmetric spreads of each element of a fuzzy vector solution are derived by solving such an interval system. Moreover, based on the obtained symmetric spreads we derive three types of solutions. However, one of the mentioned spreads has pessimistic/optimistic attitude that is determined with a decision maker. It seems that such a solution is a connection solution between Tolerable Solution Set (TSS) and Controllable Solution Set (CSS). Also, we derive the maximal solution and the minimal solution of an original fuzzy linear system which are placed in TSS and CSS, respectively. Finally, some numerical examples are given to illustrate the efficiency and ability of the proposed method.
•Considering a high-order nonlinear Schrödinger equation in a non-Kerr law media with the weak non-local nonlinearity.•Extracting some real and imaginary parts of the model using a wave variable ...transformation.•The modified Kudryashov method and symbolic computations are adopted to successfully retrieve optical solitons of the model.
The present paper explores a high-order nonlinear Schrödinger equation in a non-Kerr law media with the weak non-local nonlinearity describing solitons’ propagation through nonlinear optical fibers. To this end, the real and imaginary parts of the model are firstly extracted using a wave variable transformation. The modified Kudryashov method and symbolic computations are then adopted to successfully retrieve optical solitons of the model. The results presented in the current study demonstrate the great performance of the modified Kudryashov method in handling high-order nonlinear Schrödinger equations.
In the present research of magnetized plasmas, both rarefactive and compressive solitons are found to exist, based on the values of certain parameters. It has been shown in the present investigation ...that inclusion of beam temperature into the plasma is in search of the existence of both slow and fast modes for both the cases
Q
′
<
1
and
Q
′
>
1
. Furthermore, it is noteworthy to point out that the ion-acoustic soliton is found to exist for
γ
=
U
d
sin
θ
M
=
beam velocity
phase velocity
=
1
as well.
This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help ...explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach.
In the present work, the generalized complex Ginzburg–Landau (GCGL) model is considered and its 1-soliton solutions involving different wave structures are retrieved through a series of newly ...well-organized methods. More exactly, after considering the GCGL model, its 1-soliton solutions are obtained using the exponential and Kudryashov methods in the presence of perturbation effects. As a case study, the effect of various parameter regimes on the dynamics of the dark and bright soliton solutions is analyzed in three- and two-dimensional postures. The validity of all the exact solutions presented in this study has been examined successfully through the use of the symbolic computation system.
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