Lump chains in the KP‐I equation. Issue 4 (12th July 2021)

• Record Type: Journal Article
• Authors: Lester, Charles; Gelash, Andrey; Zakharov, Dmitry; Zakharov, Vladimir
• Is Part Of: Studies in applied mathematics. Volume 147:Issue 4(2021)
• Page Start: 1425
• Page End: 1442
• Publication Date: 2021-07-12
• Subjects: Grammian form -- line‐solitons -- lump solutions -- tau‐function; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12420
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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.