Darboux Transformation for Drinfel'd–Sokolov–Wilson Equation

Isothermal vapour-liquid equilibrium data at 65, 73 and 80 °C and isobaric ones at 101.3 kPa were measured in the tetrachloromethane-sec-butyl alcohol system. A modified circulation still of the Gillespie type was used for the measurements. Under the conditions of measurement, the system exhibits positive deviations from Raoult's law and minimum boiling-point azeotropes. The experimental data were fitted to a number of correlation equations, the most suitable being the Wilson equation.

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On Temperature Dependence of Excess Gibbs Energy

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19991093 ◽

1999 ◽

Vol 64 (7) ◽

pp. 1093-1099 ◽

Cited By ~ 2

Author(s):

Ivona Malijevská ◽

Anatol Malijevský

Keyword(s):

Heat Capacity ◽

Gibbs Energy ◽

Temperature Dependence ◽

Excess Gibbs Energy ◽

Excess Enthalpy ◽

Excess Heat Capacity ◽

Wilson Equation ◽

Excess Heat ◽

Energy Excess ◽

Wilson And Nrtl Equations

Temperature dependence of GE is discussed for three widely used equations linear and nonlinear in parameters. It is shown that the Wilson equation predicts always positive excess heat capacity regardless of values of its parameters. Several temperature modifications of the Redlich-Kister, Wilson and NRTL equations are discussed with respect to the sign of the excess Gibbs energy, excess enthalpy and excess heat capacity.

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N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽

10.3390/math9070733 ◽

2021 ◽

Vol 9 (7) ◽

pp. 733

Author(s):

Yu-Shan Bai ◽

Peng-Xiang Su ◽

Wen-Xiu Ma

Keyword(s):

Exact Solutions ◽

Gauge Transformation ◽

Darboux Transformation ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Lax Pairs ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

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Darboux transformation for classical acoustic spectral problem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120330105x ◽

2003 ◽

Vol 2003 (49) ◽

pp. 3123-3142 ◽

Cited By ~ 3

Author(s):

A. A. Yurova ◽

A. V. Yurov ◽

M. Rudnev

Keyword(s):

Spectral Problem ◽

Inhomogeneous Medium ◽

Darboux Transformation ◽

Maxwell Equations ◽

Soliton Solutions ◽

Moutard Transformation ◽

Acoustic Problem ◽

Spatial Dimensions ◽

Dielectric Permitivity ◽

Harry Dym Equation

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a nonlinear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing-chain approach, we build a modified Harry Dym equation together with its LA pair. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.

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