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Zhu, Junyi; Zhou, Sishou; Qiao, Zhijun

Forced \((2+1)\)-dimensional discrete three-wave equation. (English) Zbl 1452.35164

Commun. Theor. Phys. 72, No. 1, Article ID 015004, 7 p. (2020).
Summary: We generalize the \(\bar{\partial}\)-dressing method to investigate a \((2+1)\)-dimensional lattice, which can be regarded as a forced \((2+1)\)-dimensional discrete three-wave equation. The soliton solutions to the \((2+1)\)-dimensional lattice are given through constructing different symmetry conditions. The asymptotic analysis of one-soliton solution is discussed. For the soliton solution, the forces are zero.

Cited in 6 Documents

MSC:

35Q51 Soliton equations
35C08 Soliton solutions
34K10 Boundary value problems for functional-differential equations

Keywords:

discrete \((2+1)\)-dimensional three-wave equation; \(\bar{\partial}\)-dressing method; explicit solution
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