A double dispersion relation for a class of nonlocal potentials

1963 ◽  
Vol 28 (4) ◽  
pp. 818-833 ◽  
Author(s):  
J. T. Cushing
Keyword(s):  
Dispersion Relation ◽  
Double Dispersion ◽  
Nonlocal Potentials

Some analytic properties of three-pion decay amplitudes

1962 ◽  
Vol 266 (1324) ◽  
pp. 68-83 ◽  
Keyword(s):  
Dispersion Relation ◽  
Spectral Function ◽  
Decay Amplitude ◽  
Dispersion Relations ◽  
Pion Decay ◽  
Physical Domain ◽  
Physical Sheet ◽  
Double Dispersion ◽  
Double Spectral Function

It is shown for all graphs of the ‘strip approximation’ that the K ->3n decay amplitude obeys a Mandelstam double-dispersion relation. The double spectral function turns out to be complex and covers the whole physical domain, so that the Cini-Fubini approximation is no longer valid. Essential singularities are found on the border of the physical sheet. Double-dispersion relations in one energy and in the K mass are also derived.

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

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