scholarly journals Differential invariants and group classification of variable coefficient generalized Gardner equation

2009 ◽  
Vol 58 (10) ◽  
pp. 6686
Author(s):  
Guo Mei-Yu ◽  
Gao Jie

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous


2018 ◽  
Vol 11 (4) ◽  
pp. 747-757 ◽  
Author(s):  
Rafael de la Rosa ◽  
◽  
María Santos Bruzón


Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous


Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 83
Author(s):  
Oke Davies Adeyemo ◽  
Chaudry Masood Khalique

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.



2013 ◽  
Vol 94 (108) ◽  
pp. 81-90 ◽  
Author(s):  
Olena Vaneeva ◽  
Alexander Zhalij

The group classification of variable coefficient quasilinear reaction diffusion equations ut = uxx + h(x)B(u) is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformations within the class.



2020 ◽  
Vol 491 (1) ◽  
pp. 124215
Author(s):  
Stanislav Opanasenko ◽  
Alexander Bihlo ◽  
Roman O. Popovych


2014 ◽  
Vol 47 (4) ◽  
pp. 045201 ◽  
Author(s):  
Oksana Kuriksha ◽  
Severin Pošta ◽  
Olena Vaneeva


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