Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-bubble Bourgain-Wang solutions to nonlinear Schr\"odinger equation   We consider a general class of focusing $L^2$-critical nonlinear
Schr\"odinger equations with lower order perturbations, for which the
pseudo-conformal symmetry and the conservation law of energy are absent. In
dimensions one and two, we construct Bourgain-Wang type solutions concentrating
at $K$ distinct singularities, $1\leq K<\infty$, and prove that they are unique
if the asymptotic behavior is within the order $(T-t)^{4+}$, for $t$ close to
the blow-up time $T$. These results apply to the canonical nonlinear
Schr\"odinger equations and, through the pseudo-conformal transform, in
particular yield the existence and conditional uniqueness of non-pure
multi-solitons. Furthermore, through a Doss-Sussman type transform, these
results also apply to stochastic nonlinear Schr\"odinger equations, where the
driving noise is taken in the sense of controlled rough path.

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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci