Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations
Lili Huang,Yong Chen,Yong Chen +2 more
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TLDR
Several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction in the reduced Maxwell–Bloch equations.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2019-02-01 and is currently open access. It has received 28 citations till now. The article focuses on the topics: Lie point symmetry & Breather.read more
Citations
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A (2+1)-dimensional KdV equation and mKdV equation: Symmetries, group invariant solutions and conservation laws
Gangwei Wang,Abdul H. Kara +1 more
TL;DR: In this article, the (2+1)-dimensional KdV and mKdV equations were analyzed on the basis of the extended Lax pair and the symmetry generators were determined.
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Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation
Xiangyu Yang,Rong Fan,Biao Li +2 more
TL;DR: In this article, the authors investigate the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics.
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Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrödinger equation
TL;DR: In this article, the authors investigated the modulation instability, rogue wave and spectral analysis for the nonlinear Schrodinger equation with higher-order terms and derived the higherorder rational solutions based on the generalized Darboux transformation method.
References
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Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
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Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
Journal ArticleDOI
Intense few-cycle laser fields: Frontiers of nonlinear optics
Thomas Brabec,Ferenc Krausz +1 more
TL;DR: In this article, the authors present the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discuss the impact of these pulses on high-field physics.
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Optical rogue waves
TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.
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Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation
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