In the present paper, seventh order Caudrey-Dodd-Gibbon (CDG) equation is solved by Lie symmetry analysis. All geometry vector fields of KdV equations are presented. Using transformation CDG reduced into ordinary differential equations. These ODEs power series method to obtain exact solution. The convergence also discussed.

We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA’s and SCA’s and quaternionic and superquaternionic symmetric spaces of simple ...

We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA’s and SCA’s and quaternionic and superquaternionic symmetric spaces of simple ...

The method of nonlinear realizations is a convenient tool for building dynamical Lie group, which relies solely upon structure relations the corresponding algebra. goal this work to discuss advantages and limitations method, here applied construct perfect fluid equations with conformal symmetry. Four cases are studied in detail, include Schr\"odinger $\ensuremath{\ell}$-conformal Galilei Lifshi...

The Lagrange-d’Alembert equations of a non-holonomic system with symmetry can be reduced to the Lagrange-d’Alembert-Poincaré equations. In a previous contribution we have shown that both sets of equations fall in the category of so-called ‘Lagrangian systems on a subbundle of a Lie algebroid’. In this paper, we investigate the special case when the reduced system is again invariant under a new ...

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called λ-symmetries (C. Muriel and J. L. Romero, IMA J. Appl. Math. 66, 111-125, 2001). The notion of covering for an ODE Y is used here to recover λ-symmetries of Y as nonlocal symmetries. In this framework, by embedding Y into a suitable system Y ′ determined by the function λ, any λ-symmetry of Y can be recove...

In the present paper, PT-symmetric extension of fifth-order Korteweg-de Vries-like equation are investigated. Several special equations with PT symmetry obtained by choosing different values, for which their symmetries simultaneously. particular, particular equation, its conservation laws obtained, including momentum and energy. Reciprocal Ba¨cklund transformations energy presented first time. ...

Every smooth second-order scalar ordinary differential equation (ODE) that is solved for the highest derivative has an infinite-dimensional Lie group of contact symmetries. However, symmetries other than point symmetries are generally difficult to find and use. This paper deals with a class of one-parameter Lie groups of contact symmetries that can be found and used. These symmetry groups have ...

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group G. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundl...