Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method
We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2 versions of KP equations with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov and derived general determinant formula for such solutions. We demo...
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Zusammenfassung: | We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2
versions of KP equations with integrable boundary condition
$u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of
Zakharov and Manakov and derived general determinant formula for such
solutions. We demonstrated how reality and boundary conditions for the field
$u$ in the framework of $\overline\partial$-dressing method can be exactly
satisfied. Here we present explicit examples of two-lump solutions with
integrable boundary as nonlinear superpositions of two more simpler "deformed"
one-lump solutions: the fulfillment of boundary condition leads to formation of
certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of
standing waves on string with fixed end points. |
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DOI: | 10.48550/arxiv.2003.01716 |