[图书][B] Handbook of nonlinear partial differential equations: exact solutions, methods, and problems

AD Polyanin, VF Zaitsev - 2003 - taylorfrancis.com
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

[图书][B] Lie symmetry analysis of fractional differential equations

MS Hashemi, D Baleanu - 2020 - taylorfrancis.com
The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

Lie symmetry analysis, new group invariant for the (3+ 1)-dimensional and variable coefficients for liquids with gas bubbles models

MR Ali, R Sadat - Chinese Journal of Physics, 2021 - Elsevier
The explored solutions described some different solutions as, Lump soliton, a solitary wave
and exponential solutions. These solutions are investigated through some new Lie …

[图书][B] Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications

R Cherniha, M Serov, O Pliukhin - 2017 - taylorfrancis.com
It is well known that symmetry-based methods are very powerful tools for investigating
nonlinear partial differential equations (PDEs), notably for their reduction to those of lower …

[图书][B] Separation of variables and exact solutions to nonlinear PDEs

AD Polyanin, AI Zhurov - 2021 - taylorfrancis.com
Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and
applying methods of generalized and functional separation of variables used to find exact …

Admissible transformations and normalized classes of nonlinear Schrödinger equations

RO Popovych, M Kunzinger, H Eshraghi - Acta applicandae mathematicae, 2010 - Springer
The theory of group classification of differential equations is analyzed, substantially
extended and enhanced based on the new notions of conditional equivalence group and …

Enhanced group analysis and conservation laws of variable coefficient reaction–diffusion equations with power nonlinearities

OO Vaneeva, AG Johnpillai, RO Popovych… - Journal of Mathematical …, 2007 - Elsevier
A class of variable coefficient (1+ 1)-dimensional nonlinear reaction–diffusion equations of
the general form [Formula: see text] is investigated. Different kinds of equivalence groups …

[HTML][HTML] Extended group analysis of variable coefficient reaction–diffusion equations with exponential nonlinearities

OO Vaneeva, RO Popovych, C Sophocleous - Journal of Mathematical …, 2012 - Elsevier
The group classification of a class of variable coefficient reaction–diffusion equations with
exponential nonlinearities is carried out up to both the equivalence generated by the …

Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction–diffusion equations with variable coefficients

AD Polyanin - International Journal of Non-Linear Mechanics, 2019 - Elsevier
The paper deals with different classes of non-linear reaction–diffusion equations with
variable coefficients c (x) ut=[a (x) f (u) ux] x+ b (x) g (u), that admit exact solutions. The direct …

Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source

OO Vaneeva, RO Popovych, C Sophocleous - Acta applicandae …, 2009 - Springer
A new approach to group classification problems and more general investigations on
transformational properties of classes of differential equations is proposed. It is based on …