Formation and Interaction of Sonic-Langmuir Solitons Inverse Scattering Method
About: This article is published in Progress of Theoretical Physics.The article was published on 1976-12-01 and is currently open access. It has received 300 citations till now. The article focuses on the topics: Scattering theory & Scattering amplitude.
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TL;DR: In this paper, a coupled Korteweg-de Vries equation is presented, which exhibits a soliton solution and three basic conserved quantities for a special choice of dispersion relations.
757 citations
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TL;DR: In this article, an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates is presented.
Abstract: This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.
373 citations
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TL;DR: In this paper, it was shown that a higher-order nonlinear Schrodinger equation which describes propagation of pulses in optical fiber is solvable by means of the inverse scattering transform, which possesses a remarkable property that it can propagate steadily with two peaks of the same height.
Abstract: It is shown that a higher-order nonlinear Schrodinger equation which describes propagation of pulses in optical fiber is solvable by means of the inverse scattering transform. The soliton solution possesses a remarkable property that it can propagate steadily with two peaks of the same height.
371 citations
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TL;DR: In this article, an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates is presented.
Abstract: This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher-dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.
319 citations
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TL;DR: In this paper, the authors consider linear problems associated with integrable systems in 2+1 dimensions and obtain generating functions for symmetries from the bilocal approach. But they do not consider symmetric systems.
253 citations
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TL;DR: In this paper, the nonstationary evolution of nonlinear Langmuir waves is considered and the process of soliton formation is studied in the case where the perturbation propagates with a speed close to that of sound.
Abstract: The nonstationary evolution of nonlinear Langmuir waves is considered. In particular the process of soliton formation is studied in the case where the perturbation propagates with a speed close to that of sound. The influence of electron collisions on the motion of the soliton is also described.
67 citations
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TL;DR: Inverse scattering transforms as discussed by the authors can be used to solve the sine-Gordon equation in laboratory coordinates, which can be seen as a generalization of the direct and inverse scattering transforms.
Abstract: By solving the direct and inverse scattering problems for a rather ‘unconventional’ eigenvalue problem, we can solve the initial value problem for the sine-Gordon equation entirely in laboratory coordinates. This allows us to extend and accurately define the class of initial value problems which can be solved by ‘inverse scattering transforms.’ Simple examples are given to illustrate both the direct and the inverse scattering methods.
53 citations