Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution

1988 ◽  
Vol 27 (6) ◽  
pp. 717-723 ◽  
Author(s):  
N. Euler ◽  
P. G. L. Leach ◽  
F. M. Mahomed ◽  
W. -H. Steeb
Keyword(s):  
Field Equation ◽  
Vector Fields ◽  
Similarity Solutions ◽  
Maxwell Distribution ◽  
Nonlinear Field

Approximate Solution of a Nonlinear Field Equation

1963 ◽  
Vol 4 (3) ◽  
pp. 334-338 ◽  
Author(s):  
D. D. Betts ◽  
H. Schiff ◽  
W. B. Strickfaden
Keyword(s):  
Approximate Solution ◽  
Field Equation ◽  
Nonlinear Field

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

Analytic Lyapunov exponents in a classical nonlinear field equation

2000 ◽  
Vol 61 (4) ◽  
pp. R3299-R3302 ◽  
Author(s):  
Roberto Franzosi ◽  
Raoul Gatto ◽  
Giulio Pettini ◽  
Marco Pettini
Keyword(s):  
Field Equation ◽  
Lyapunov Exponents ◽  
Nonlinear Field

Numerical twistor procedure for solving a nonlinear field equation

1994 ◽  
Vol 35 (12) ◽  
pp. 6489-6497
Author(s):  
T. Moorhouse ◽  
R. S. Ward
Keyword(s):  
Field Equation ◽  
Nonlinear Field

A note on a positive solution of a null mass nonlinear field equation in exterior domains

2019 ◽  
Vol 150 (2) ◽  
pp. 841-870
Author(s):  
Alireza Khatib ◽  
Liliane A. Maia
Keyword(s):  
Field Equation ◽  
Positive Solution ◽  
Ground State ◽  
Bound State ◽  
Nonlinear Field ◽  
Regular Domain ◽  
Exterior Domains ◽  
Bound State Solution ◽  
Image Position ◽  
Bounded Regular Domain

AbstractWe consider the Null Mass nonlinear field equation (𝒫)$$\left\{ {\matrix{ {-\Delta u = f(u){\rm in}\;\;\Omega } \hfill \hfill \hfill \hfill \cr {u > 0} \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \cr {u \vert_{\partial \Omega } = 0} \cr } } \right.$$ where ${\open R}^N \setminus \Omega $ is a bounded regular domain. The existence of a bound state solution is established in situations where this problem does not have a ground state.

scholarly journals CONSERVED CURRENT FOR GENERAL TELEPARALLEL MODELS

2002 ◽  
Vol 17 (20) ◽  
pp. 2765-2765 ◽  
Author(s):  
Y. ITIN
Keyword(s):  
Field Equation ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Geometrical Structures ◽  
Yang Mills ◽  
First Order ◽  
Diffeomorphism Invariance ◽  
Maxwell Field Equation ◽  
Conserved Current

The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures1,2. A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑa is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity) 3. By introducing the notion of a 3-parameter conjugate field strength F linear in the strength Ca = dϑa the coframe Lagrangian is rewritten in the Maxwell-Yang-Mills form L = 1/2Fa ∧ Ca. The field equation turns out to have a form d * Fa = Ta completely similar to the Maxwell field equation. By applying the Noether procedure, the source 3-form Ta is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source Ta of the coframe field is interpreted as the total conserved energy-momentum current of the coframe field and matter4. The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields 5. Thus an energy-momentum tensor for the coframe is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in the standard GR. The result is: The standard GR has a neighborhood of viable models with the same Schwarzschild solutions. These models however have a better Lagrangian behavior and produce an invariant energy-momentum tensor.

Lie Bäcklund Vector Fields and Similarity Solutions

1991 ◽  
Vol 60 (3) ◽  
pp. 1132-1133 ◽  
Author(s):  
N. Euler ◽  
W.-H. Steeb ◽  
P. Mulser
Keyword(s):  
Vector Fields ◽  
Similarity Solutions
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