We introduce a new, to the best of our knowledge, type of band-limited optical pulse-soliton-sinc tailored to the nonlinear Schrödinger (NLS) equation. The idea behind the soliton-sinc pulse is to combine, even if approximately, a property of a fundamental soliton to propagate without distortions in nonlinear systems governed by the NLS equation with a compact band-limited spectrum of a Nyquist pulse. Though the shape preserving propagation feature is not exact, such soliton-sinc pulses are more robust against nonlinear signal distortions compared to a Nyquist pulse.
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http://dx.doi.org/10.1364/OL.402286 | DOI Listing |
J Evol Equ
December 2024
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA.
The well-posedness of the initial-boundary value problem for higher-order quadratic nonlinear Schrödinger equations on the half-line is studied by utilizing the Fokas solution formula for the corresponding linear problem. Using this formula, linear estimates are derived in Bourgain spaces for initial data in spatial Sobolev spaces on the half-line and boundary data in temporal Sobolev spaces suggested by the time regularity of the linear initial value problem. Then, the needed bilinear estimates are derived and used for showing that the iteration map defined via the Fokas solution formula is a contraction in appropriate solution spaces.
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October 2024
School of Science, Shaoyang University, Shaoyang, 422000, Hunan, People's Republic of China.
In this article, we propose a split-step finite element method (FEM) for the two-dimensional nonlinear Schrödinger equation (NLS) with Riesz fractional derivatives in space. The space-fractional NLS is first spatially discretized by finite element scheme and the semi-discrete variational scheme is obtained. We prove that it maintains the mass and energy conservation laws.
View Article and Find Full Text PDFChaos
October 2024
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Sci Rep
September 2024
Department of Mathematics, College of Science, King Saud University, 11989, Riyadh, Saudi Arabia.
In this study, the modified Sardar sub-equation method is capitalised to secure soliton solutions to the -dimensional chiral nonlinear Schrödinger (NLS) equation. Chiral soliton propagation in nuclear physics is an extremely attractive field because of its wide applications in communications and ultrafast signal routing systems. Additionally, we perform bifurcation analysis to gain a deeper understanding of the dynamics of the chiral NLS equation.
View Article and Find Full Text PDFChaos
September 2024
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China.
In this paper, we analyze the large-space and large-time asymptotic properties of the vector rogon-soliton and soliton-like solutions of the n-component nonlinear Schrödinger equation with mixed nonzero and zero boundary conditions. In particular, we find that these solutions have different decay velocities along different directions of the x axis, that is, the solutions exponentially and algebraically decay along the positive and negative directions of the x axis, respectively. Moreover, we study the change of the acceleration of soliton moving with the increase in time or distance along the characteristic line (i.
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