Bessel Functions, Recursion and a Nonlinear Field Equation

2001 ◽  
Vol 56 (9-10) ◽  
pp. 710-712
Author(s):  
Willi-Hans Steeb ◽  
Yorick Hardy ◽  
Ruedi Stoop
Keyword(s):  
Field Equation ◽  
Bessel Functions ◽  
Bäcklund Transformations ◽  
Nonlinear Field ◽  
Field Equations ◽  
Particular Solutions ◽  
Backlund Transformations ◽  
Nonlinear Field Equations

Abstract We show that particular solutions of certain nonlinear field equations can be constructed using Bäcklund transformations, recursion and Bessel functions.

A Derivation of Relativistically-Invariant Nonlinear Field Equations for Strongly Interacting Many-Body Systems

1997 ◽  
Vol 11 (07) ◽  
pp. 929-944 ◽  
Author(s):  
J. A. Tuszyński ◽  
J. M. Dixon
Keyword(s):  
Field Equation ◽  
Equations Of Motion ◽  
Nonlinear Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Relativistic Regime ◽  
Klein Gordon ◽  
Many Body Systems ◽  
Nonlinear Field Equations

We re-examine the derivation of nonlinear field equations for a system of strongly interacting quasiparticles. Emphasis is placed on typical dispersion relations in the relativistic regime. Through Heisenberg's equations of motion for second-quantised operators we demonstrate that interacting many-body systems are described by a nonlinear Klein–Gordon type field equation. Its nonrelativistic equivalent was previously shown to be of the nonlinear Schrödinger type.

On the Initiation of Necking Modes in Layered Plastic Solids

1987 ◽  
Vol 54 (1) ◽  
pp. 141-146 ◽  
Author(s):  
P. S. Steif
Keyword(s):  
Small Parameter ◽  
Finite Strain ◽  
Relative Rate ◽  
Perturbation Expansion ◽  
Nonlinear Field ◽  
Field Equations ◽  
Regular Perturbation ◽  
Layered Solid ◽  
Interface Imperfections ◽  
Nonlinear Field Equations

The deformation of a solid consisting of alternating material layers with interface undulations is studied analytically. We assess the relative rate of growth or decay of these interface imperfections with straining. The analysis is based on a regular perturbation expansion of the finite strain, nonlinear field equations, the small parameter being the amplitude of the undulations relative to the layer thickness. Attention is focused on the influence of material and geometric parameters on imperfection growth-rates. It is found that significant connections exist between the growth of imperfections and the tendency for undulatory bifurcation modes to emerge from a perfect, layered solid.

scholarly journals Tachyon inflation in an AdS braneworld with backreaction

2017 ◽  
Vol 32 (05) ◽  
pp. 1750039 ◽  
Author(s):  
Neven Bilić ◽  
Dragoljub D. Dimitrijevic ◽  
Goran S. Djordjevic ◽  
Milan Milosevic
Keyword(s):  
Free Parameter ◽  
Initial Conditions ◽  
Hamiltonian Formalism ◽  
Brane Tension ◽  
Nonlinear Field ◽  
Tachyon Field ◽  
Field Equations ◽  
Braneworld Cosmology ◽  
Wide Range ◽  
Nonlinear Field Equations

We analyze the inflationary scenario based on the tachyon field coupled with the radion of the second Randall–Sundrum model (RSII). The tachyon Lagrangian is derived from the dynamics of a 3-brane moving in the five-dimensional bulk. The AdS5 geometry of the bulk is extended to include the radion. Using the Hamiltonian formalism we find four nonlinear field equations supplemented by the modified Friedmann equations of the RSII braneworld cosmology. After a suitable rescaling we reduce the parameters of our model to only one free parameter related to the brane tension and the AdS5 curvature. We solve the equations numerically assuming a reasonably wide range of initial conditions determined by physical considerations. Varying the free parameter and initial conditions we confront our results with the Planck 2015 data.

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