相关论文: Symmetry analysis and exact solutions of semilinea…
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system…
Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrodinger equations in dimensions $n\neq 1$. Both focusing and defocusing cases of a power nonlinearity are considered,…
This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates…
Explicit solutions are obtained for a class of semilinear radial Schrodinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new…
A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
In this paper, we study the Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions. The infinitesimal generators that span the Lie algebra for this system are…
A heat equation with non-constant diffusivity depending as a power law on the spatial variable is analysed using Lie's method to identify classical point symmetries. It is shown that the group invariant solutions of a four-dimensional…
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
This study presents a new mass-lumping finite element method for computing the radially symmetric solution of a semilinear heat equation in an $N$ dimensional ball ($N\ge 2$). We provide two schemes, (ML-1) and (ML-2), and derive their…
Exact solutions for nonlinear Arrhenius reaction-diffusion are constructed in $n$ dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term leads to a nonclassical Lie symmetry whose invariant solutions…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…