Related papers: Group classification of variable coefficient gener…
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…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
We calculate the first extension groups for finite-dimensional simple modules over an arbitrary generalized current Lie algebra, which includes the case of loop Lie algebras and their multivariable analogs.
Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears a crucial point for the exhaustive solution of the problem. We prove that all the…
In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent…
In this paper, a generalized variable-coefficient KdV equation (vcKdV) arising in fluid mechanics, plasma physics and ocean dynamics is investigated by using symmetry group analysis. Two basic generators are determined, and for every…
We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by…
We suggest a method of constructing special nonunitary representations of semisimple Lie groups using representations of Iwasawa subgroups. As a typical example, we study the group $U(2,2)$.
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
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.
In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type…
We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f),…
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential 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 normalized class of differential equations. Effective new techniques…
The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.
We study the Jimbo-Miwa equation and two of its extended forms, as proposed by Wazwaz et al, using Lie's group approach. Interestingly, the travelling-wave solutions for all the three equations are similar. Moreover, we obtain certain new…
We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the…