Add to ORKGWe study integrability of a system of nonlinear partial differential equations consis-ting 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 cases when it is compati-ble. The results obtained can be applied, in particular, to construct principally new (non-Lie, non-similarity) solutions of the non-linear d’Alembert, Dirac, and Yang-Mills equations. Solutions found in this way are shown to correspond to conditional symmetry of the equations enumerated above. Using the said approach, we stu...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
M.Sc.In this work we concentrate on two generalizations of Lie symmetries namely conditional symmetr...
"As long as algebra and geometry proceded along separate paths, their advance was slow and their ap...
The study deals with multidimensional nonlinear wave equations. The work is aimed at studying Lie an...
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs...
AbstractThe necessary conditions of the compatibility of the d'Alembert-Hamilton system in Minkowsky...
A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional red...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
Bäcklund transformations between all known completely integrable third-order differential equations ...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
The work covers the non-linear differential equations. The aim is to classify the quasi-linear hyper...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
As an example of how to deal with nonintegrable systems, the nonlinear partial dif-ferential equatio...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
M.Sc.In this work we concentrate on two generalizations of Lie symmetries namely conditional symmetr...
"As long as algebra and geometry proceded along separate paths, their advance was slow and their ap...
The study deals with multidimensional nonlinear wave equations. The work is aimed at studying Lie an...
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs...
AbstractThe necessary conditions of the compatibility of the d'Alembert-Hamilton system in Minkowsky...
A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional red...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
Bäcklund transformations between all known completely integrable third-order differential equations ...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
The work covers the non-linear differential equations. The aim is to classify the quasi-linear hyper...
The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\...
As an example of how to deal with nonintegrable systems, the nonlinear partial dif-ferential equatio...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
Nonlinear partial differential equations play a fundamental role in the description of many physical...
M.Sc.In this work we concentrate on two generalizations of Lie symmetries namely conditional symmetr...
"As long as algebra and geometry proceded along separate paths, their advance was slow and their ap...