Oblique plane waves with bifurcation behaviors and chaotic motion for resonant nonlinear Schrodinger equations having fractional temporal evolution

Hafez, M. G.; Iqbal, Sayed Allamah; Akther, S.; Uddin, Mesbah

doi:10.1016/j.rinp.2019.102778

Cited by 31 publications

(6 citation statements)

References 37 publications

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“…For oblique interaction of nonlinear structures, such picture is easier to investigate the system properties. [41,48,49] The angle between two ion acoustic solitons can be described as,…”

Section: Mathematical Modelmentioning

confidence: 99%

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Hasan

Masood

Jahangir

et al. 2021

Contributions to Plasma Physics

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We have investigated the interaction of obliquely propagating ion acoustic solitary waves in a magnetoplasma with relativistically degenerate electrons. Using the quantum hydrodynamics model and by employing the extended Poincaré-Lighthill-Kuo technique, we have derived a set of Korteweg de Vries equations for two solitons. We have observed that the system under consideration allows the formation of only compressive solitons and their velocities remain in the sub-acoustic limit. Furthermore, phase shifts of solitons as a result of their interaction have been calculated. The phase shifts have been observed to be dependent on the obliqueness and the physical parameters of plasma. It has also been noticed that phase shifts remain negative for the whole range of parameters generally found in white dwarf stars. We have observed that the phase shifts enhance with the enhancement in number density, however, the converse happens when the magnetic field is enhanced. It has also been observed that the phase shift is slightly greater for the solitons that are less oblique as compared to their more oblique counterparts. Furthermore, we have estimated the spatial scales of interaction of solitons using the parameters found in white dwarf stars. K E Y W O R D Snonlinear structures, quantum plasma, solitons INTRODUCTIONRelativistically degenerate plasmas have engendered research interest in the past few decades. Dense plasmas have enormous applications in different situations like nanostructures, white dwarf stars, and other such extreme conditions. [1][2][3][4][5][6][7][8][9][10] At high pressure and low temperature, the electron degeneracy effects become important in order to study the properties of plasma systems. [11] In such conditions, the electron Fermi energy level rises above the thermal energy level. Therefore, electron Fermi energy level becomes dominant in order to investigate different properties of plasma. The coupling of the quantum scale properties with the large-scale astrophysical objects like white dwarf stars creates interesting areas of plasma systems. For instance, the electron degeneracy on the quantum scale can get coupled with the stability of astrophysical objects such as white dwarf stars. A balance is created between degeneracy pressure caused by the Pauli exclusion principle and the gravitational pull of the white dwarf star. The pulsations in the white dwarf stars originate from gravity (g-mode) waves, [12,13] whereas the observation of compressional (p-mode) waves is still awaited. [14] In these dense environments, the electron equation of state changes from P ∼ n 5/3 to P ∼ n 4/3 and in these circumstances the white dwarf star can become gravitationally unstable. [15,16] Such instabilities modify the oscillation spectrum of the core of white dwarf star, which enables us to study the properties of dense plasma. [17]

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“…For oblique interaction of nonlinear structures, such picture is easier to investigate the system properties. [41,48,49] The angle between two ion acoustic solitons can be described as,…”

Section: Mathematical Modelmentioning

confidence: 99%

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Hasan

Masood

Jahangir

et al. 2021

Contributions to Plasma Physics

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“…It is noted that

represents the normalized complex amplitude of the wave profile. Many research scholars [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] have devoted significant effort to revealing various types of traveling wave solutions for mathematical physics equations like Eq. (1) by considering many environments via several types of theoretical and computational architectures.…”

Section: Introductionmentioning

confidence: 99%

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

Uddin

Hafez

Iqbal

2022

Heliyon

Self Cite

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“…The development of BFD and CFD meet many features of fundamental calculus, whereas the earlier fractional derivatives does not support some features of fundamental calculus. In References [33][34][35][36][37][38], authors have been used such derivatives for describing a wide range of physical processes. For instance, Uddin et al [33][34][35][36] have reported that the effect of BFD parameter on nonlinear wave phenomena by considering different kinds of environments.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Uddin et al [33][34][35][36] have reported that the effect of BFD parameter on nonlinear wave phenomena by considering different kinds of environments. Hafez et al [37] and Iqbal et al [38] have reported that the effect of CFD parameter on wave phenomena with their dynamical features in optical bullets and one-dimensional nonlinear electrical transmission line, respectively. It is now required to investigate nonlocal and nonconservative physical issues in optical fibers due to imperfections/nonuniformities in birefringent fibres along with some technical challenges resulting from fiber technologies discussed previously.…”

Section: Introductionmentioning

confidence: 99%

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

Uddin

Hafez

2022

Advances in Mathematical Physics

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The work explores the optical wave solutions along with their graphical representations by proposing the coupled spatial-temporal fractional cubic-quartic nonlinear Schrödinger equation with the sense of two fractal derivatives (beta and conformable derivative) and Kerr law nonlinearity for birefringent fibers. The new extended direct algebraic method for the first time is implemented to achieve this goal. Many optical solutions are listed along with their existence criteria. Based on the existence criteria, the cubic-quartic bright, and singular optical soliton, periodic pulse, and rouge wave profiles are supported in birefringent fibers with the influence of both beta and conformable derivative parameter.

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Oblique plane waves with bifurcation behaviors and chaotic motion for resonant nonlinear Schrodinger equations having fractional temporal evolution

Cited by 31 publications

References 37 publications

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

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