Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On invariance properties of the wave equation (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 307-318 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete group classification is given of both the wave equation c2(x)uxx−utt=0 (I) and its equivalent system vt=ux, c2(x)vx=ut (II) when the wave speed c(x)≠const. Equations (I) and (II) admit either a two- or four-parameter group. For the exceptional case, c(x)=(Ax+B)2, equation (I) admits an infinite group. Equations (I) and (II) do not always admit the same group for a given c(x): The group for (I) can have more parameters or fewer parameters than that for (II); moreover, the groups can be different with the same number of parameters. Separately for (I) and (II), all possible c(x) that admit a four-parameter group are found explicitly. The corresponding invariant (similarity) solutions are considered. Some of these wave speeds have realistic physical properties: c(x) varies monotonically from one positive constant to another positive constant as x goes from −∞ to +∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527659
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Exact solutions for wave equations of two-layered media with smooth transition (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 86-96 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The wave equation c2(x)uxx−utt=0 is solved for wave speeds c(x) corresponding to two-layered media with smooth transition from layer to layer. The wave speed c(x) has four free parameters to fit a given medium. Solutions are constructed from invariant solutions of a related system of first-order partial differential equations that admit a four-parameter symmetry group. These solutions are superposed to solve general initial value problems for data with compact support; the computation of the superposition coefficients uses elementary Fourier analysis. Solutions are illustrated for various initial conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528137
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Derivation of conservation laws from nonlocal symmetries of differential equations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2361-2375 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An identity is derived which yields a correspondence between symmetries and conservation laws for self-adjoint differential equations. This identity does not rely on use of a Lagrangian as needed to obtain conservation laws by Noether's theorem. Moreover, unlike Noether's theorem, which can only generate conservation laws from local symmetries, the derived identity generates conservation laws from nonlocal as well as local symmetries. It is explicitly shown how Noether's theorem is extended by the identity. Conservation laws arising from nonlocal symmetries are obtained for a class of scalar wave equations with variable wave speeds. The constants of motion resulting from these nonlocal conservation laws are shown to be linearly independent of all constants of motion resulting from local conservation laws. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531515
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    New classes of symmetries for partial differential equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 806-811 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: New classes of symmetries for partial differential equations are introduced. By writing a given partial differential equation S in a conserved form, a related system T with potentials as additional dependent variables is obtained. The Lie group of point transformations admitted by T induces a symmetry group of S. New symmetries may be obtained for S that are neither point nor Lie–Bäcklund symmetries. They are determined by a completely algorithmic procedure. Significant new symmetries are found for the wave equation with a variable wave speed and the nonlinear diffusion equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527974
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3508-3532 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nonlocal symmetries are obtained for Maxwell's equations in three space–time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space–time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space–time dimensions. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531866
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    The use of factors to discover potential systems or linearizations (1995)
    Springer
    Acta applicandae mathematicae 41 (1995), S. 21-43 
    Details
    ISSN: 1572-9036
    Keywords: 35A30 ; 58G35 ; 35K55 ; 22E65 ; 58B25 ; nonlocal symmetries ; potential symmetries ; linearization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Factors of a given system of PDEs are solutions of an adjoint system of PDEs related to the system's Fréchet derivative. In this paper, we introduce the notion of potential conservation laws, arising from specific types of factors, which lead to useful potential systems. Point symmetries of a potential system could yield nonlocal symmetries of the given system and its linearization by a noninvertible mapping. We also introduce the notion of linearizing factors to determine necessary conditions for the existence of a linearization of a given system of PDEs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00996104
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    facet.materialart.
    Unknown
    Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws (2008)
    Details
    Publication Date: 2020-08-05
    Description: An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...