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arXiv · 1108.2956

The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles

Shmuel Fishman·Yevgeny Krivolapov·Avy Soffer
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Abstract

The Nonlinear Schroedinger Equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a random (Anderson like) potential has been done at various levels of control: numerical, analytical and rigorous. Yet, this model equation presents us with a highly inconclusive and often contradictory picture. We will describe the main recent results obtained in this field and propose a list of specific problems to focus on, that we hope will enable to resolve these outstanding questions.

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Shmuel Fishman, Yevgeny Krivolapov, Avy Soffer. 2011-08-15. The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles. https://doi.org/10.1088/0951-7715%2F25%2F4%2Fr53

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