Lump chains in the KP‐I equation

We construct a broad class of solutions of the Kadomtsev–Petviashvili (KP)‐I equation by using a reduced version of the Grammian form of the τ‐function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities. More generally, our solutions are evolv...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2021-11, Vol.147 (4), p.1425-1442
Main Authors: Lester, Charles, Gelash, Andrey, Zakharov, Dmitry, Zakharov, Vladimir
Format: Article
Language:English
Subjects:
Chains
Grammian form
line‐solitons
lump solutions
Solitary waves
tau‐function
Wave propagation
Wave velocity
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Summary:We construct a broad class of solutions of the Kadomtsev–Petviashvili (KP)‐I equation by using a reduced version of the Grammian form of the τ‐function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities. More generally, our solutions are evolving linear arrangements of lump chains, and can be viewed as the KP‐I analogues of the family of line‐soliton solutions of KP‐II. However, the linear arrangements that we construct for KP‐I are more general, and allow degenerate configurations such as parallel or superimposed lump chains. We also construct solutions describing interactions between lump chains and individual lumps, and discuss the relationship between the solutions obtained using the reduced and regular Grammian forms.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12420