New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves

Alam, Md. Nur; Osman, M. S.

doi:10.1088/1572-9494/abd849

Cited by 20 publications

(2 citation statements)

References 41 publications

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“…The authors in [16] have used Lie symmetries and used ¢ ( ) G G -expansion modified method. The last method had been applied also in [17,18] to solve the Boussinesq equation and a dynamical equations model related to the ion sound and Langmuir waves. Geophysical flows and nonlinear optics are governed by coupled nonlinear Schrödinger equations (CNLSEs) as in [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

Elbrolosy

2021

Phys. Scr.

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This work is interested in constructing new traveling wave solutions for the coupled nonlinear Schrödinger type equations. It is shown that the equations can be converted to a conservative Hamiltonian traveling wave system. By using the bifurcation theory and Qualitative analysis, we assign the permitted intervals of real propagation. The conserved quantity is utilized to construct sixteen traveling wave solutions; four periodic, two kink, and ten singular solutions. The periodic and kink solutions are analyzed numerically considering the affect of varying each parameter keeping the others fixed. The degeneracy of the solutions discussed through the transmission of the orbits illustrates the consistency of the solutions. The 3D and 2D graphical representations for solutions are presented. Finally, we investigate numerically the quasi-periodic behavior for the perturbed system after inserting a periodic term.

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Section: Introductionmentioning

confidence: 99%

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

Elbrolosy

2021

Phys. Scr.

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“…It can be seen from literature [1][2][3][4][5][6][7] that the first step of these authors was to reduce the STO equation of the fractional order to a nonlinear ordinary differential equation by using fractional complex transformation and then to solve the reduced equation by various methods to obtain the solution of the original fractional-order equation. In addition to the methods provided in literature [1][2][3][4][5][6][7], there are other techniques that can be used to obtain wave solutions of different structures [14][15][16][17][18][19]. It can be seen from equations ( 1)-( 3) that the most general equation is equation ( 1), so we only discuss the accurate general traveling wave solution of equation (1).…”

Section: Introductionmentioning

confidence: 99%

General Traveling Wave Solutions of Nonlinear Conformable Fractional Sharma-Tasso-Olever Equations and Discussing the Effects of the Fractional Derivatives

Fan

Wang

Zhou

2021

Advances in Mathematical Physics

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The exact traveling wave solution of the fractional Sharma-Tasso-Olever equation can be obtained by using the function expansion method, but the general traveling wave solution cannot be obtained. After transforming it into the Sharma-Tasso-Olever equation of the integer order by the fractional complex transformation, the general solution of its traveling wave is obtained by a specific function transformation. Through parameter setting, the solution of the kinked solitary wave is found from the general solution of the traveling wave, and it is found that when the two fractional derivatives become smaller synchronically, the waveform becomes more smooth, but the position is basically unchanged. The reason for this phenomenon is that the kink solitary wave reaches equilibrium in the counterclockwise and clockwise rotation, and the stretching phenomenon is accompanied in the process of reaching equilibrium. This is a further development of our previous work, and this kind of detailed causative analysis is rare in previous papers.

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Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

et al. 2021

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Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea and are hard to be predicted. Although nonlinear Schrödinger equation (NLS) provides a perspective, it alone can neither detect rogue waves nor provide a complete solution to problems. Therefore, some approximations are still mandatory for both obtaining an exact solution and predicting rogue waves. Such as Kundu-Mukherjee-Naskar (KMN) model which allows obtaining lump-soliton solutions considered as rogue waves. In this study the functional variable method is utilized to obtain the analytical solutions of KMN model that corresponds to the propagation of soliton dynamics in optical fiber communication system.

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New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves

Abstract: This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves. The modified ( G ′ / G ) -expansion procedure is utilized to raise new closed-form wave solutions. Those s… Show more

Cited by 20 publications

References 41 publications

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

General Traveling Wave Solutions of Nonlinear Conformable Fractional Sharma-Tasso-Olever Equations and Discussing the Effects of the Fractional Derivatives

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

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