We study integrability of a system of nonlinear partial differential equations consisting of the nonlinear d’Alembert equation 2u = F (u) and nonlinear eikonal equation uxμuxμ = G(u) in the complex Minkowski space R(1, 3). A method suggested makes it possible to establish necessary and sufficient compatibility conditions and construct a general solution of the d’Alembert-eikonal system for all ...

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related with the classical shallow water model with the change of variables. The derived symmetries are used to generate new exact solutions of the rotating shallow eq...

We study a two-dimensional integrable generalization of the Kaup-Kupershmidt equation, which arises in various problems in mathematical physics. Exact solutions are obtained using the Lie symmetry method in conjunction with the extended tanhmethod and the extended Jacobi elliptic functionmethod. In addition to exact solutions we also present conservation laws which are derived using the multipl...

We incorporate the new theory of equivariant moving frames for Lie pseudo-groups into Vessiot’s method of group foliation of differential equations. The automorphic system is replaced by a set of reconstruction equations on the pseudo-group jets. The result is a completely algorithmic and symbolic procedure for finding both invariant and non-invariant solutions of differential equations admitti...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting-based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence uni...

A new method of constructing structure equations of Lie symmetry pseudo-groups of differential equations, dispensing with explicit solutions of the (infinitesimal) determining systems of the pseudo-groups, is presented, and illustrated by the examples of the Kadomtsev–Petviashvili and Korteweg–de-Vries equations.

A twist field on a cylindrical space–time has the defining property that translation about a spatial circle results in multiplying the field by a phase. In this paper we investigate how such multivalued twist fields fit into the framework of constructive quantum field theory. Twisted theories have an interest in their own right; the twists also serve as infrared regulators that partially preser...

g/u(1) d parafermions from constrained WZNW theories. Abstract The conformal field theory based on the g/u(1) d coset construction is treated as the WZNW theory for the affine Lie algebrâ g with the constrainedû(1) d subalgebra.Using a modification of the generalized canonical quantization method generators and primary fields of an extended symmetry algebra are found for arbitrary d.

Abstract The extended Kadomtsev-Petviashvili (eKP) equation in fluids is investigated by using Lie symmetry analysis. reductions, together with the simplest method, are used to obtain exact solutions of eKP equation. Finally, we derive conservation laws multiplier approach.