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

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

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

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.

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.

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