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N-fold Darboux transformation and conservation laws of the modified Volterra lattice

Department of Applied Mathematics, University of Science and Technology Beijing, Beijing 100083, China

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

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Yong-Li Sun

http://orcid.org/0000-0002-9177-9448

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China

E-mail Address: sunyl@mail.buct.edu.cn

Corresponding author.

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, and

Chaudry Masood Khalique

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

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https://doi.org/10.1142/S0217984918504092Cited by:14 (Source: Crossref)

Abstract

In this work, we study the modified Volterra lattice. Applying the gauge transformation of the associated $2 \times 2$ matrix spectral problems, we establish the N-fold Darboux transformation (DT), and then construct a few explicit solutions in terms of determinants upon using the obtained DT. Moreover, all the results are illustrated by the graphs of the solitonic evolution profiles of the aforementioned solutions. Finally, infinitely many conservation laws for the modified Volterra lattice are proposed. The obtained results of this research might be applied to the research on nonlinear phenomena in physics or engineering areas.

Keywords:

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