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Wang, Xueru; Zhu, Junyi; Qiao, Zhijun

New solutions to the differential-difference KP equation. (English) Zbl 1458.35021

Appl. Math. Lett. 113, Article ID 106836, 8 p. (2021).
Summary: In this paper, we study the differential-difference Kadomtsev-Petviashvili (D\(\varDelta\)KP) equation through the dressing method based on a nonlocal \(\overline{\partial} \)-problem. Cauchy type determinant solution and a new type rational solution are given. The initial value problem of D\(\varDelta\)KP is discussed by virtue of the quasi-local \(\overline{\partial}\)-problem. From an impulse initial condition, a new explicit solution to the initial value problem of D\(\varDelta\)KP is obtained.

Cited in 7 Documents

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35R09 Integro-partial differential equations

Keywords:

\(\overline{\partial}\)-dressing method; D\(\varDelta\)KP equation; nonlocal \(\overline{\partial}\)-problem; Kadomtsev-Petviashvili; impulse initial condition
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References:

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