M‐Breather, Lumps, and Soliton Molecules for the (2 + 1)‐Dimensional Elliptic Toda Equation

Yuechen Jia, Yu Lu, Miao Yu and Hasi Gegen

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: The (2 + 1)‐dimensional elliptic Toda equation is a higher dimensional generalization of the Toda lattice and also a discrete version of the Kadomtsev‐Petviashvili‐1 (KP1) equation. In this paper, we derive the M‐breather solution in the determinant form for the (2 + 1)‐dimensional elliptic Toda equation via Bäcklund transformation and nonlinear superposition formulae. The lump solutions of the (2 + 1)‐dimensional elliptic Toda equation are derived from the breather solutions through the degeneration process. Hybrid solutions composed of two line solitons and one breather/lump are constructed. By introducing the velocity resonance to the N‐soliton solution, it is found that the (2 + 1)‐dimensional elliptic Toda equation possesses line soliton molecules, breather‐soliton molecules, and breather molecules. Based on the N‐soliton solution, we also demonstrate the interactions between a soliton/breather‐soliton molecule and a lump and the interaction between a soliton molecule and a breather. It is interesting to find that the KP1 equation does not possess a line soliton molecule, but its discrete version—the (2 + 1)‐dimensional elliptic Toda equation—exhibits line soliton molecules.

Date: 2021
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https://doi.org/10.1155/2021/5211451

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:5211451

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