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This paper investigates the new coupled $$(2+1)$$ (2+1) -dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method. Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons...
The degenerate coupled multi-Korteweg–de Vries equations for coupled multiplicity $$l=3$$ l=3 are studied. The equations, also known as three-field Kaup–Boussinesq equations, are considered for invariant analysis and conservation laws. The classical Lie’s symmetry method is used to analyse the symmetries of equations. Based on the Killing’s form, which is invariant of adjoint action, the full classification...
In this paper, we study Klein–Gordon–Zakharov equations which describe the propagation of strong turbulence of the Langmuir wave in a high-frequency plasma. Using the symbolic manipulation tool Maple, the classifications of symmetry algebra are carried out, and the construction of several local non-trivial conservation laws based on a direct method of Anco and Bluman is illustrated. Starting with...
A theoretical model is described here for studying the effect of temperature on nanomaterials. The thermodynamic equation of state (EoS) proposed by Goyal and Gupta in High Temp.-High Press.45, 163 (2016); Oriental J. Chem.32(4), 2193 (2016), is extended in the present study using Qi and Wang model [Mater. Chem. Phys.88, 280 (2004)]. The thermal expansion coefficient is expressed in terms of shape...
In this paper, variable coefficient Benny equation (also called the KdV Burgers–Kuramoto equation) has been considered. By using the Painlevé analysis and Lie group analysis methods, the Painlevé properties and symmetries have been studied. Some solutions of the reduced ODEs are obtained.
In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G′/G)-expansion method, where...
In the present paper we have pointed out the weaknesses of the approach by Aynyas et al [1] to study the structural phase transition and elastic properties of thorium pnictides. The calculated values of phase transition pressure and other elastic properties using the realistic and actual approach are also given and compared with the experimental and previous theoretical work.
In the present investigation we have explained the thermal and compression properties of HCP iron (Fe) at high pressure with variable temperature (isobars) and at high temperature with variable pressure (isotherm). The usual Tait equation of state is modified by incorporating the effect of thermal pressure. The calculated values of pressure for different isotherms and isochors and thermal expansivity...
The equation of state is a fundamental relation to analyse the thermophysical properties of different class of solids and it plays a key role in basic and applied condensed matter physics research. A lot of work has been done in the field of ionic solids, minerals and metals but a very little work is done in the field of inert gas solids. Most of the equations of state failed to explain the properties...
A simple and very efficient gas jet levitation technique for levitating inertial confinement fusion (ICF) targets has been developed. A low velocity gas jet through diverging nozzle generates precisely controlled low Reynolds number flow pattern, capable of levitating polymer microballoons up to 2500 µm diameter. Different shaped diverging nozzle are investigated, satisfactory levitation is achieved...
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