This review summarizes all known results (up to this date) about methods of integration of
the classical Lotka–Volterra systems with diffusion and presents a wide range of exact …

A self-contained introduction to the methods and techniques of symmetry analysis used to
solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents …

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 …

This study is devoted to a class of linear and nonlinear differential equations with fractional-
order governing diffusion, Burger's, Airy's, KdV, gas dynamic and Fisher's equations. These …

The diffusive Lotka–Volterra system arising in an enormous number of mathematical models
in biology, physics, ecology, chemistry and society is under study. New Q-conditional …

The nonclassical symmetries method is applied to a class of reaction-diffusion equations
with nonlinear source, ie ut= u xx+ cu x+ R (u, x). Several cases are obtained by using …

Q-conditional symmetries of the classical diffusive Lotka–Volterra system in the case of one
space variable are completely described and a set of such symmetries in explicit form is …

Beta-ensembles of random matrices are naturally considered as quantum integrable
systems, in particular, due to their relation with conformal field theory, and more recently …

Q-conditional symmetries (nonclassical symmetries) for the general class of two-component
reaction–diffusion systems with non-constant diffusivities are studied. Using the recently …

New Q-conditional (nonclassical) symmetries and exact solutions of the hunter-gatherer–
farmer population model proposed by Aoki et al.(Theor. Popul. Biol. 50, 1–17) are …