THERMAL SCIENCE

International Scientific Journal

Sheng ZhangORCID

,

Di WangORCID

A TODA LATTICE HIERARCHY WITH VARIABLE COEFFICIENTS AND ITS MULTI-WAVE SOLUTIONS

ABSTRACT
Starting from the Toda spectral problem, a new Toda lattice hierarchy of isospectral equations with variable coefficients is constructed through the discrete zero curvature equation. In order to solve one special case of the derived Toda lattice hierarchy, a series of appropriate transformations are utilized. As a result, a new uniform formula of N-wave solutions is obtained.
KEYWORDS
Toda lattice hierarchy, isospectral equation, zero curvature equation, multi-wave solution
PAPER SUBMITTED: 2013-09-29
PAPER REVISED: 2014-05-07
PAPER ACCEPTED: 2014-07-23
PUBLISHED ONLINE: 2015-01-04
DOI REFERENCE: https://doi.org/10.2298/TSCI1405563Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE No. 5, PAGES [1563 - 1566]
REFERENCES
[1] Liu, Y., et al., Multi-Soliton Solutions of the Forced Variable-Coefficient Extended Korteweg-de Vries Equation Arisen in Fluid Dynamics of Internal Solitary Waves, Non-linear Dynamics, 66 (2011), 4, pp. 575-587, 10.1007/s11071-010-9936-7
[2] Yu, F. J., A Real Non-Linear Integrable Coupling for Generalized Toda Soliton Hierarchy, Acta Mathematica Scientia, 35 (2012), 5, pp. 974-981
[3] Lee, N. C., et al., A Note on Reductions of the Dispersionless Toda Hierarchy, Journal of Mathematical Physics, 51 (2012), 12, 122704, 10.1063/1.3524508
[4] Helminck, G. F., et al., Equivalent Forms of Multi Component Toda Hierarchies, Journal of Geometry and Physics, 61 (2011), 4, pp. 847-873, 10.1016/j.geomphys.2010.11.013
[5] Chen, D. Y., Introduction to Soliton, Science Press, Beijing, China, 2006
[6] Zhang, S., Zhang, H. Q., Exp-Function Method for N-Soliton Solutions of Non-Linear Differential- Difference Equations, Zeitschrift fur Naturforschung A, 65 (2010), 11, pp. 924-934, 10.1515/zna-2010-1105
PDF VERSION [DOWNLOAD]
A Toda lattice hierarchy with variable coefficients and its multi-wave solutions

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence