Lagrangian formulation of a generalized Lane-Emden equation and double reduction

Khalique, Chaudry Masood; Mahomed, F. M.; Muatjetjeja, Ben

doi:10.2991/jnmp.2008.15.2.3

Cited by 55 publications

(34 citation statements)

References 35 publications

(37 reference statements)

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“…Its general solution is given by Eq. (29) and we recover the solution given in (50). Only a one-parameter family of solutions is known in the other literature, namely, y =[ 3a/(x 2 + 3a 2 )] 1/2 , a = constant (see, e.g., (27) or (51)).…”

Section: If Nmentioning

confidence: 55%

The Lane-Emden equation and its generalizations

Khalique¹

2012

Astrophysics

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where r is a constant, models the thermal behaviour of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed by Lane (1) (see also (3)) and studied in detail by Emden (2). Fowler (4; 5) considered a generalization of Eq. (1), called Emden-Fowler equation (6), where the last term is replaced by x ν−1 y r .The Lane-Emden equation (1) also models the equilibria of nonrotating fluids in which internal pressure balances self-gravity. When spherically symmetric solutions of Eq. (1) appeared in (7), they got the attention of astrophysicists. In the latter half of the twentieth century, some interesting applications of the isothermal solution (singular isothermal sphere) and its nonsingular modifications were used in the structures of collisionless systems such as globular clusters and early-type galaxies (8; 9).The work of Emden (2) also got the attention of physicists outside the field of astrophysics who investigated the generalized polytropic forms of the Lane-Emden equation (1) for specific polytropic indices r. Some singular solutions for r = 3 were produced by Fowler (4; 5) and the Emden-Fowler equation in the literature was established, while the works of Thomas (10) and Fermi (11) (29)). Usually, for r = 5, only a one-parameter family of solutions is presented. A more general form of (1), in which the

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Section: If Nmentioning

confidence: 55%

The Lane-Emden equation and its generalizations

Khalique¹

2012

Astrophysics

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“…The Noether symmetries of Eq. (1) were investigated in [12] and exact solutions for various cases which admitted Noether point symmetries were obtained. Some other works on symmetries and solutions of Lane-Emden-type equations can be found in [13][14][15][16][17][18][19] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian approach to a generalized coupled Lane–Emden system: Symmetries and first integrals

Muatjetjeja¹,

Khalique²

2010

Communications in Nonlinear Science and Numerical Simulation

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“…It is well known that many well known methods have been established in scientific fields and engineering to determine the solutions with distinct physical structures [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Examples of the methods that have been used are the Hirota bilinear method, the simplified Hirota's method, the Bäcklund transformation method, Darboux transformation, Pfaffian technique [7][8][9][10], the inverse scattering method, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method [13][14][15][16][17][18][19][20], the mapping and the deformation approach and many other methods [20][21][22][23][24][25][26][27].…”

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confidence: 99%