scholarly journals On comparison of asymptotic expansion techniques for nonlinear Klein-Gordon equation in the nonrelativistic limit regime

2020 ◽  
Vol 25 (8) ◽  
pp. 2841-2865
Author(s):  
Katharina Schratz ◽  
◽  
Xiaofei Zhao ◽  
◽  
Keyword(s):  
Asymptotic Expansion ◽  
Gordon Equation ◽  
Nonrelativistic Limit ◽  
Klein Gordon ◽  
Nonrelativistic Limit Regime ◽  
Klein Gordon Equation

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the Woods–Saxon potential is solved. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for any l-states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

scholarly journals A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

2005 ◽  
Vol 02 (01) ◽  
pp. 77-89 ◽  
Author(s):  
HANS LINDBLAD ◽  
AVY SOFFER
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Long Range ◽  
Gordon Equation ◽  
Scattering Problem ◽  
One Dimension ◽  
Complete Asymptotic Expansion ◽  
Arbitrary Size ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider the scattering problem for the nonlinear Klein–Gordon Equation with long range nonlinearity in one dimension. We prove that for all prescribed asymptotic solutions there is a solution of the equation with such behavior, for some choice of initial data. In the case the nonlinearity has the good sign (repulsive) the result hold for arbitrary size asymptotic data. The method of proof is based on reducing the long range phase effects to an ODE; this is done via an appropriate ansatz. We also find the complete asymptotic expansion of the solutions.

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