Some novel optical pulses in hydrodynamical nonlinear complex equation using M-truncated fractional derivative. [PDF]
Ilhan E +4 more
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Exploring highly dispersive optical solitons and modulation instability in nonlinear Schrödinger equations with nonlocal self phase modulation and polarization dispersion. [PDF]
Hasan WM +4 more
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Sub pico-second pulses in mono-mode optical fibers with Triki-Biswas model. [PDF]
Hussain A +5 more
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Accelerated Diffusion Basis Spectrum Imaging With Tensor Computations. [PDF]
Utt KL, Blum JS, Rim D, Song SK.
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Dynamical behavior of analytical solutions and bifurcation analysis for a novel structured (2+1)-dimensional Kadomtsev-Petviashvili equation via analytic approach. [PDF]
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Singularities of Solutions of Singular Integral Equations
Ukrainian Mathematical Journal, 2002This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
Kapustyan, V. E., Il'man, V. M.
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Singular vacuum solutions as singular matter solutions: Where do spacetime singularities come from?
EPL (Europhysics Letters), 2017A direct evidence for the existence of spacetime singularities is the existence of singularities in vacuum solutions of the Einstein equation. A singular vacuum solution implies that spacetime itself may have singularities. In this paper, we exemplify that a singular vacuum solution can also serve as a non-vacuum solution of the Einstein equation with ...
Yu-Zhu Chen, Wu-Sheng Dai
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