[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 …
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 …
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
The explored solutions described some different solutions as, Lump soliton, a solitary wave
and exponential solutions. These solutions are investigated through some new Lie …
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 …
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 …
applying methods of generalized and functional separation of variables used to find exact …
Admissible transformations and normalized classes of nonlinear Schrödinger equations
The theory of group classification of differential equations is analyzed, substantially
extended and enhanced based on the new notions of conditional equivalence group and …
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
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 …
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
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 …
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 …
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
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 …
transformational properties of classes of differential equations is proposed. It is based on …