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Multidimensional Solitons: Theory

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Emergent Nonlinear Phenomena in Bose-Einstein Condensates

Part of the book series: Atomic, Optical, and Plasma Physics ((SSAOPP,volume 45))

The one-dimensional solitons described in Parts II and III of this book can be extended into two and three dimensions. Such extensions are generally unstable [1]. However, in the tightly confined geometries associated with trapped Bose-Einstein condensates (BECs) both bright and dark solitons extended into two and three dimensions can be stabilized for times longer than the lifetime of experiments [2–4]. BECs offer the opportunity to tune a matter-wave gradually from one to two and to three dimensions [5, 6]. In the crossover regimes, new nonlinear objects can appear, such as the svortex, a solitary wave which is a soliton-vortex hybrid [7, 8]. The general question of crossover dimensions is an intriguing one in physics.

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  1. Colorado School of Mines, 80401, Golden, CO, USA

    L. D. Carr

  2. Massey University, Auckland, New Zealand

    J. Brand

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  1. University of Massachusetts, Amherst, MA, 01003-4515, USA

    Panayotis G. Kevrekidis

  2. University of Athens, Athens, 15784, Greece

    Dimitri J. Frantzeskakis

  3. San Diego State University, San Diego, CA, 92182-7720, USA

    Ricardo Carretero-González

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Carr, L.D., Brand, J. (2008). Multidimensional Solitons: Theory. In: Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R. (eds) Emergent Nonlinear Phenomena in Bose-Einstein Condensates. Atomic, Optical, and Plasma Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73591-5_7

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