Mixed solutions for an AB system in geophysical fluids or nonlinear optics

Learning dominant physical processes with data-driven balance models

Nature Communications ◽

10.1038/s41467-021-21331-z ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 2

Author(s):

Jared L. Callaham ◽

James V. Koch ◽

Bingni W. Brunton ◽

J. Nathan Kutz ◽

Steven L. Brunton

Keyword(s):

Nonlinear Optics ◽

Unsupervised Learning ◽

History Of Science ◽

Traditional Approach ◽

Data Driven ◽

Mechanistic Models ◽

Physical Processes ◽

History Of ◽

Separation Of Scales ◽

Geophysical Fluids

AbstractThroughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

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Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics

Modern Physics Letters B ◽

10.1142/s0217984918500392 ◽

2018 ◽

Vol 32 (04) ◽

pp. 1850039 ◽

Cited By ~ 4

Author(s):

Xi-Yang Xie ◽

Gao-Qing Meng

Keyword(s):

Nonlinear Optics ◽

Soliton Solutions ◽

Dark Soliton ◽

Elastic Collision ◽

Mean Flow ◽

Short Pulses ◽

Dark Solitons ◽

Parameter Measuring ◽

The One ◽

Geophysical Fluids

Under investigation in this paper is a coupled AB system, which describes the marginally unstable baroclinic wave packets in the geophysical fluids or ultra-short pulses in nonlinear optics. As the dark solitons are more resistant against various perturbations than the bright ones, we aim to investigate the dark solitons in the geophysical fluids or nonlinear optics. Dark one- and two-soliton solutions for such a system are derived based on the bilinear forms and propagations of the one solitons and collisions between the two solitons are graphically illustrated and analyzed. Further, influences of the coefficients [Formula: see text] and [Formula: see text] on the solitons are discussed, where [Formula: see text] is a parameter measuring the state of the basic flow and [Formula: see text] is the group velocity. The dark-one solitons with invariant shapes and amplitudes are viewed, and elastic collisions between the dark-two solitons are observed. Also, elastic collision between the bright and dark solitons is viewed, and the dark soliton is found to possess two peaks. [Formula: see text] is found to affect the widths of the dark-one solitons and the travelling directions of the dark-two solitons. It is shown that [Formula: see text] cannot influence shapes of [Formula: see text] and [Formula: see text], but affect the plane of the one soliton for [Formula: see text], and the two-peak dark soliton for [Formula: see text] changes to the single-peak one with the value of [Formula: see text] decreasing, where [Formula: see text] and [Formula: see text] are the packets of short waves and [Formula: see text] is the mean flow.

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