Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly interacting multi-solitons with logarithmic relative distance
  for gKdV equation   We consider the following class of equations of (gKdV) type $$\partial_t u +
\partial_x (\partial_x^2 u + |u|^{p-1}u) = 0, \quad p\mbox{ integer},\quad t,x
\in \mathbb{R}$$ with mass sub-critical ($2< p<5$) and mass super-critical
nonlinearities ($p> 5$). We prove the existence of 2-solitary wave solutions
with logarithmic relative distance, i.e. solutions $u(t)$ satisfying
\[\left\|u(t)- \bigg( Q (\cdot - t - \log (ct)) + \sigma Q (\cdot - t + \log
(ct))\bigg)\right\|_{H^1}\to 0 \ \ \mbox{as} \ \ t\to +\infty,\] where $c=c(p)>
0$ is a fixed constant, $\sigma = -1$ in sub-critical cases and $\sigma = 1$ in
super-critical cases. For the integrable case ($p=3$), such solution was known
by integrability theory. This regime corresponds to strong attractive
interactions. For sub-critical $p$, it was known that opposite sign traveling
waves are attractive. For super-critical $p$, we derive from our computations
that same sign traveling waves are attractive.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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