New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

Ghanbari, Behzad; Gómez‐Aguilar, J.F.

doi:10.1142/s021798491950235x

Cited by 93 publications

(22 citation statements)

References 24 publications

(31 reference statements)

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“…The Ginzburg-Landau (GL) equation [1][2][3][4][5][6][7] is one of the most important partial differential equations in the field of mathematics and physics, which was introduced into the study of superconductivity phenomenology theory in the 20th century by Ginzburg and Landau. The GL equation usually describes the optical soliton [8][9][10][11][12][13][14][15] propagation through optical fibers over longer distances. Therefore, it is very important to analyze the dynamic behavior of the GL equation.…”

Section: Introductionmentioning

confidence: 99%

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

Han

2021

Advances in Mathematical Physics

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In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

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Section: Introductionmentioning

confidence: 99%

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

Han

2021

Advances in Mathematical Physics

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“…On the other hand, the progress of rogue ionacoustic behaviours in many distributed electrons have been investigated [15,16]. Generally, many theoretical studies in solitary applications in natural science and space have been reported [16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Nonlinearity contributions on critical MKP equation

Abdelwahed

2020

Journal of Taibah University for Science

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The mathematical new plasma wave solutions are specified in the compose of trigonometric, rational, hyperbolic, periodic and explosive kinds that are realistic for Modified-Kadomtsev-Petviashvili (MKP) equation. Also, numeral studies for the acquired solutions have been reveals that periodic, shock and explosive new forms may applicable in D-F Earth's ionosphere plasma. The used method is influential and robust in comparison applications in plasma fluids. To depict the propagating soliton profiles in a plasma medium, it is needful to solve MKP equation at a critical mass ratio. The Riccati-Bernoulli sub-ODE technique has been utilized to introduce some new important and applicable solutions. The number of these MKP solutions give a leading deed in applied ion acoustics in ionosphere.

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“…For instance, one of the important research areas in modern applied mathematics is the theory of non-integer derivative. Particularly in engineering sciences, fractional derivatives are a very powerful tool for modeling many problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On the relations between some well-known methods and the projective Riccati equations

Akçağıl

2020

Open Physics

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Solving nonlinear evolution equations is an important issue in the mathematical and physical sciences. Therefore, traditional methods, such as the method of characteristics, are used to solve nonlinear partial differential equations. A general method for determining analytical solutions for partial differential equations has not been found among traditional methods. Due to the development of symbolic computational techniques many alternative methods, such as hyperbolic tangent function methods, have been introduced in the last 50 years. Although all of them were introduced as a new method, some of them are similar to each other. In this study, we examine the following four important methods intensively used in the literature: the tanh–coth method, the modified Kudryashov method, the F-expansion method and the generalized Riccati equation mapping method. The similarities of these methods attracted our attention, and we give a link between the methods and a system of projective Riccati equations. It is possible to derive new solution methods for nonlinear evolution equations by using this connection.

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New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

Cited by 93 publications

References 24 publications

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

Nonlinearity contributions on critical MKP equation

On the relations between some well-known methods and the projective Riccati equations

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