scholarly journals Nonlinear Schrödinger-type formulation of scalar field cosmology: Two barotropic fluids and exact solutions

2020 ◽  
Vol 35 (19) ◽  
pp. 2050157
Author(s):  
Chonticha Kritpetch ◽  
Jarunee Sanongkhun ◽  
Pichet Vanichchapongjaroen ◽  
Burin Gumjudpai
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Time Dependent ◽  
Frw Cosmology ◽  
Dependent Case ◽  
Nonlinear Schrödinger ◽  
Barotropic Fluids ◽  
Scalar Field Cosmology ◽  
Formulation Variables ◽  
Canonical Scalar Field

Time-independent nonlinear Schrödinger-type (NLS) formulation of FRW cosmology with canonical scalar field is considered in the case of two barotropic fluids. We derived Friedmann formulation variables in terms of NLS variables. Seven exact solutions found by D’Ambroise [Ph.D. thesis, arXiv:1005.1410 ] and one new found solution are explored and tested in cosmology. The result suggests that time-independent NLS formulation of cosmology case should be upgraded to the time-dependent case.

scholarly journals EXACT SOLUTIONS FOR COSMOLOGICAL MODELS WITH A SCALAR FIELD

2002 ◽  
Vol 17 (03) ◽  
pp. 375-381 ◽  
Author(s):  
H. MOTAVALI ◽  
M. GOLSHANI
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Cosmological Models ◽  
Coupling Function ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Frw Cosmology ◽  
Field Equations ◽  
Tensor Theory ◽  
Cosmological Solutions

We consider the existence of a Noether symmetry in the scalar–tensor theory of gravity in flat Friedman–Robertson–Walker (FRW) cosmology. The forms of coupling function ω(ϕ) and generic potential V(ϕ) are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.

Exact solutions in string-motivated scalar-field cosmology

1992 ◽  
Vol 45 (4) ◽  
pp. R997-R999 ◽  
Author(s):  
Murat Özer ◽  
M. O. Taha
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Field Cosmology

scholarly journals Exact Solutions to the Nonlinear Schrödinger Equation with Time-Dependent Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Xin-Lei Mai ◽  
Wei Li ◽  
Shi-Hai Dong
Keyword(s):  
Exact Solutions ◽  
Optical Fibers ◽  
Time Dependent ◽  
Jacobi Elliptic Function ◽  
Optical Pulses ◽  
Nonlinear Schrödinger ◽  
Ultrashort Optical Pulses ◽  
Trial Function Method ◽  
High Order Time ◽  
Special Case

In this paper, a trial function method is employed to find exact solutions to the nonlinear Schrödinger equations with high-order time-dependent coefficients. This system might be used to describe the propagation of ultrashort optical pulses in nonlinear optical fibers, with self-steepening and self-frequency shift effects. The new general solutions are found for the general case a 0 ≠ 0 including the Jacobi elliptic function solutions, solitary wave solutions, and rational function solutions which are presented in comparison with the previous ones obtained by Triki and Wazwaz, who only studied the special case a 0 = 0 .

A new look at the Schrödinger equation in exact scalar field cosmology

2019 ◽  
Vol 16 (02) ◽  
pp. 1950022 ◽  
Author(s):  
I. V. Fomin ◽  
S. V. Chervon ◽  
S. D. Maharaj
Keyword(s):  
Wave Function ◽  
Scalar Field ◽  
Exact Solutions ◽  
Closed Form ◽  
Generating Function ◽  
Hubble Parameter ◽  
Scalar Potential ◽  
Scale Factor ◽  
Simple Transformation ◽  
Scalar Field Cosmology

We propose a new representation of the Schrödinger-like equation for scalar field Friedmann cosmology where the scalar field is the argument, and the Hubble parameter is the analogue to the wave function. Such an approach gives us the possibility to use the Schrödinger potential as a generating function which leads to generalization of known exact solutions. Further, we find a simple transformation of the Hubble parameter which generates new solutions from the Schrödinger-like equation. Several examples are identified where exact forms for the scale factor, Hubble parameter and scalar potential can be written in closed form. Earlier results are regained in our approach.

scholarly journals Noether symmetry approach for Dirac–Born–Infeld cosmology

2015 ◽  
Vol 12 (05) ◽  
pp. 1550065 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Ratbay Myrzakulov
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Interaction Potential ◽  
Noether Symmetry ◽  
Symmetry Approach ◽  
Canonical Scalar Field

We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field T with a Dirac–Born–Infeld Lagrangian and a potential V(T). Furthermore, we assume a coupled canonical scalar field ϕ with an arbitrary interaction potential B(T, ϕ). Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.

scholarly journals DILATION DARK MATTER IN VAIDYA–de SITTER SPACETIME

1999 ◽  
Vol 08 (06) ◽  
pp. 719-724 ◽  
Author(s):  
NEACSU MARIA CRISTINA
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Mass Parameter ◽  
Time Dependent ◽  
Static Case ◽  
De Sitter ◽  
Field Equations ◽  
Dependent Case ◽  
Relativistic Star ◽  
De Sitter Universe

The exterior of a relativistic star can be modeled with the Vaidya radiating metric. It is started from the generalized Vaidya metric that allows a type II fluid and studied the conditions of generating new analytical solutions of the Einstein's field equations. It is shown that the mass parameter solution gives the classical de Sitter universe in the static case and the extended de Sitter metric coupled with a dilation scalar field in the time-dependent case. It is concluded that in the time-dependent case the atmosphere of a relativistic star consists on an anisotropic string fluid coupled with a dark matter null fluid and interpreted the scalar field as the particle that produces the dark matter.

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