Geometrical interpretation of solutions of certain PDEs
نویسندگان
چکیده
In §1 the authors define the notion of harmonic map between two generalized Lagrange spaces. In §2 it is proved that for certain systems of differential or partial differential equations, the solutions belong to a class of harmonic maps between two generalized Lagrange spaces. §3 describes the main properties of the generalized Lagrange spaces constructed in §2. These spaces, being convenient relativistic models, allow us to write the Maxwell’s and Einstein’s equations. Mathematics Subject Classification: 53C60, 49N45, 35R30.
منابع مشابه
Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...
متن کاملPerturbative techniques for integrable systems
There are two main approaches to the perturbative study of integrable PDEs: 1) perturbations of linear PDEs and 2) perturbations of nonlinear integrable systems of hydrodynamic type. In the talk we will mainly consider the problems and results related to the second approach. After explaining the main geometrical techniques such as the group of generalized Miura transformations, the idea of quas...
متن کاملA New Technique of Reduce Differential Transform Method to Solve Local Fractional PDEs in Mathematical Physics
In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...
متن کاملMultiphase Computations in Geometrical Optics
In this work we propose a new set of partial diierential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases. The traditional geometrical optics pair of equations suuer from the fact that the class of physically relevant solutions is limited. In particular, it does not include solutions with multipl...
متن کاملAsymptotic scaling symmetries for nonlinear PDEs
In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large x and/or t) invariant under a group G which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential equations – and solution-preserving maps – we provide a precise definition of asymptotic symmetries of PDEs; we deal in particular, for ease of discussion and physica...
متن کامل