Stability of Solitary Waves for the Generalized Klein–Gordon–Hartree Equation

2019 ◽  
Author(s):  
Boyan Kostadinov ◽  
Mirko Tarulli ◽  
George Venkov
Keyword(s):  
Solitary Waves ◽  
Hartree Equation ◽  
Klein Gordon ◽  
Stability Of Solitary Waves

scholarly journals Instability of solitary waves for the generalized Klein–Gordon–Hartree equation

2019 ◽  
Author(s):  
Boyan Kostadinov ◽  
Mirko Tarulli ◽  
George Venkov
Keyword(s):  
Solitary Waves ◽  
Hartree Equation ◽  
Klein Gordon

EXISTENCE AND STABILITY OF SOLITARY WAVES IN NON-LINEAR KLEIN–GORDON–MAXWELL EQUATIONS

2006 ◽  
Vol 18 (07) ◽  
pp. 747-779 ◽  
Author(s):  
EAMONN LONG
Keyword(s):  
Solitary Waves ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Topological Solitons ◽  
Weakly Coupled ◽  
Non Linear ◽  
Existence And Stability ◽  
Klein Gordon ◽  
Stability Of Solitary Waves

We prove the existence and stability of non-topological solitons in a class of weakly coupled non-linear Klein–Gordon–Maxwell equations. These equations arise from coupling non-linear Klein–Gordon equations to Maxwell's equations for electromagnetism.

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.

Sign in / Sign up

Export Citation Format

Share Document