Related papers: Conditional Symmetry and Reductions for the Two-Di…
We present full classification of Q-conditional symmetries for the two-dimensional nonlinear wave equation.
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…
Some aspects of $Q$-conditional symmetry and of its connections with reduction and compatibility are discussed.
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…
We study conditions of reduction of multidimensional wave equations - a system of d'Alembert and Hamilton equations. Necessary conditions for compatibility of such reduction conditions are proved. Possible types of the reduced equations and…
We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the…
We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and Tzitzeica equations.…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…
We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the…
In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…
The definition of Q-conditional symmetry for one PDE is correctly generalized to a special case of systems of PDEs and involutive families of operators. The notion of equivalence of Q-conditional symmetries under a group of local…
We present the iterative classical point symmetry analysis of a shallow water wave equation in $2+1$ dimensions and that of its corresponding nonisospectral, two component Lax pair. A few reductions arise and are identified with celebrate…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…