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The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

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Abstract

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential–difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

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Acknowledgements

The author would like to express her gratitude to the referee for valuable suggestions. This work was supported by the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2016MS0115), the National Natural Science Foundation of China (Grant Nos. 11601247 and 11605096).

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  1. School of Mathematical Science, Inner Mongolia University, No. 235 West College Road, Hohhot, 010021, Inner Mongolia, People’s Republic of China

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Gegenhasi The modified semi-discrete two-dimensional Toda lattice with self-consistent sources. Anal.Math.Phys. 9, 99–118 (2019). https://doi.org/10.1007/s13324-017-0184-6

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