Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation arising in dusty plasma

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

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Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients

Nonlinear Dynamics ◽

10.1007/s11071-021-06284-8 ◽

2021 ◽

Vol 104 (1) ◽

pp. 639-648 ◽

Cited By ~ 2

Author(s):

Tukur Abdulkadir Sulaiman ◽

Abdullahi Yusuf ◽

Marwan Alquran

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Optical Solitons ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Complex Wave

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Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0054 ◽

2020 ◽

Vol 21 (7-8) ◽

pp. 675-681

Author(s):

Rehab M. El-Shiekh ◽

Mahmoud Gaballah

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Integration Method ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Equation Method ◽

Direct Integration ◽

Wave Solutions ◽

Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

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