Higher Symmetries of the Elliptic Euler-darboux Equation
نویسنده
چکیده
We find a remarkable subalgebra of higher symmetries of the elliptic Euler-Darboux equation. To this aim we map such equation into its hyperbolic analogue already studied by Shemarulin. Taking into consideration how symmetries and recursion operators transform by this complex contact transformation, we explicitly give the structure of this Lie algebra and prove that it is finitely generated. Furthermore, higher symmetries depending on jets up to second order are explicitly computed.
منابع مشابه
Adomian Decomposition Method On Nonlinear Singular Cauchy Problem of Euler-Poisson- Darbuox equation
n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem.
متن کاملMultiplicity result to some Kirchhoff-type biharmonic equation involving exponential growth conditions
In this paper, we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity. Using some variational arguments and exploiting the symmetries of the problem, we establish a multiplicity result giving two nontrivial solutions.
متن کاملVESSIOT STRUCTURE FOR MANIFOLDS OF (p, q)-HYPERBOLIC TYPE: DARBOUX INTEGRABILITY AND SYMMETRY
It is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is Darboux integrable, then its local Cauchy problem may be solved by ordinary differential equations. In addition, such an equation has infinitely many non-trivial conservation laws. Moreover, Darboux integrable equations have properties in common with infinite dimensional compl...
متن کاملNew Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries
In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process. This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process.
متن کاملCauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler–Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated t...
متن کامل