Related papers: Exact Solutions of G-Invariant Chiral Equations
We show how realization theory can be used to find the solutions of the Carath\'eodory extremal problem on the symmetrized bidisc \[ G \stackrel{\rm{def}}{=} \{(z+w,zw):|z|<1, \, |w|<1\}. \] We show that, generically, solutions are unique…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to study different examples and use…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
A direct and systematic algorithm is proposed to find one-dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra. Since the method is based on…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
We suggest a method for integrating sub-families of a family of nonlinear {\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries. Since the…
A Lie group $G$ endowed with a left invariant Riemannian metric $g$ is called Riemannian Lie group. Harmonic and biharmonic maps between Riemannian manifolds is an important area of investigation. In this paper, we study different aspects…
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
In this paper, first we study carefully the positive solutions to $\Delta u+\lambda_{1}u\ln u +\lambda_{2}u^{b+1}=0$ defined on a complete noncompact Riemannian manifold $(M, g)$ with $Ric(g)\geq -Kg$, which can be regarded as…
The present article studies the potential form of the nonlinear Gardner-Kawahara equation through the perspective of Lie symmetry analysis. Lie symmetry analysis was used to investigate abundant group-invariant solutions of the nonlinear…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of…
Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=\pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The…
A numerical method to solve linear integro-differential equations is presented. This method has been used to solve the QCD Altarelli-Parisi evolution equations within the H1 Collaboration at DESY-Hamburg. Mathematical aspects and numerical…
We develop the theory of equivariant harmonic self-maps of compact cohomogeneity one manifolds and construct new harmonic self-maps of the compact Lie groups SO(4L+2), L >= 1, with degree -3, of SO(8), SO(14) and SO(26) with degree -5 each,…
We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For…
We describe an algorithm for determining the algebraic subgroup of GL(n,C) that is defined as the closure of the group generated by a finite number of elements of GL(n,C). The algorithm avoids the use of Groebner bases and can be used on…