New nonautonomous combined multi-wave solutions for ( $$\varvec{2+1}$$ 2 + 1 )-dimensional variable coefficients KdV equation

Osman, M. S.; Machado, J. A. Tenreiro

doi:10.1007/s11071-018-4222-1

Cited by 73 publications

(7 citation statements)

References 31 publications

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“…where u = u(x, t) shows the traveling wave profile, depending on the space of the independent variables x and time t. In Equation (1), the first term indicates the linear evaluation of the phenomena, the coefficient of σ represents the spatio-temporal dispersion (STD) and the coefficient of ρ shows the group velocity dispersion (GVD). The perturbation terms appear on the right-hand side of Equation (1). The coefficient of κ represents the inter-model dispersion, the coefficient of δ shows the self-steepening perturbation term and the coefficient indicates the nonlinear dispersion, while p is the full nonlinearity parameter.…”

Section: Model and Methods Descriptionmentioning

confidence: 99%

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Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

et al. 2021

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This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power, dual power law, triple power law, quadratic–cubic law and anti-cubic law. The dark, bright, singular and combinations of these solutions are retrieved using an efficient, simple integration scheme. These solutions suggest that this method is more simple, straightforward and reliable compared to existing methods in the literature. The novelty of this paper is that the perturbed nonlinear Schrödinger equation is investigated in different nonlinear media using a novel derivative operator. Furthermore, the numerical simulation for certain solutions is also presented.

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Section: Model and Methods Descriptionmentioning

confidence: 99%

“…Finding solitary wave solutions is the most interesting work in soliton theory [1,2]. Many physical phenomena are represented as prototypes in the form of nonlinear partial differential equations (PDEs), particularly in nonlinear Schrödinger equations (NSEs).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

et al. 2021

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“…For more resources and conclusions concerning to the fractional-order derivative and its scientific applications, one can come back to the accompanying fortunes. [51][52][53][54][55][56][57][58][59][60][61][62] Example 3. Meditate the accompanying cost functional…”

Section: Solutions Of Fractional-order Ocpsmentioning

confidence: 99%

Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis

Arqub

Shawagfeh

2019

Math Methods in App Sciences

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Modeling of dynamic systems of optimal control problems (OCPs) is very important issue in applied sciences and engineering. In this analysis, by developed the reproducing kernel Hilbert space (RKHS) method within the calculus of variations, the OCP is solved with respect to initial conditions and Fredholm operator optimality. The solution methodology involves the use of two generalized Hilbert spaces (HSs) for both range and domain spaces. Numerical algorithm and procedure of solution are assembled compatibility with the optimal formulation of the problem. The convergence analysis and error rating of the utilized method are considered under some presumptions, which provide the theoretical structure behind the technique. The optimal profiles show the performance of the numerical solutions and the effect of the Fredholm operator in the optimal results. In this approach, computational simulations are introduced to delineate the suitability, straightforwardness, and relevance of the calculations created.

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“…Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. Many researchers have provided solutions to different types of these equations as in (Baskonus et al 2021;Akbar et al 2021;Osman and Machado 2018;Abdel-Gawad and Osman 2015;Kumar et al 2021;Osmana et al 2020;Osman 2018;; GaziKarakoc and Ali 2020; Karakoc and and which characterize ion-acoustic waves in a cold-ion plasma but where the electrons do not behave isothermally during their passage of the wave. Parkes (1999, 2000) demonstrate that if the electrons are non-isothermal, the ZK equation is a modified form (mZK) equation.…”

Section: Introductionmentioning

confidence: 99%

Computational and analytical solutions to modified Zakharov–Kuznetsov model with stability analysis via efficient techniques

Ali

Mehanna²

2021

Opt Quant Electron

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In this paper, we present the analytic and numerical solutions of the newly modified Zakharov-Kuznetsov equation. This model is used to study the waves in different plasmas. The analytical solutions were achieved by the extended tanh method and the Sine Gordon method while the numerical one is achieved by the implicit finite difference method and the local truncation error and the stability analysis for the difference scheme are given. Graphical representations of exact and numerical solutions are given to illustrate our results. In addition to the other known results in the literature, the paper contributes new analytical and numerical results.

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New nonautonomous combined multi-wave solutions for ( $$\varvec{2+1}$$ 2 + 1 )-dimensional variable coefficients KdV equation

Cited by 73 publications

References 31 publications

Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis

Computational and analytical solutions to modified Zakharov–Kuznetsov model with stability analysis via efficient techniques

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