Orbital stability of solitary waves for the Klein-Gordon-Zakharov equations

1999 ◽  
Vol 15 (1) ◽  
pp. 54-64 ◽  
Author(s):  
Chen Lin
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Klein Gordon ◽  
Stability Of Solitary Waves

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.

scholarly journals Solitons for the Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
J. Bellazzini ◽  
V. Benci ◽  
C. Bonanno ◽  
A.M. Micheletti
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Energy Charge ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Field Equations ◽  
Klein Gordon ◽  
Ratio Energy ◽  
Klein Gordon Equation

AbstractIn this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.

scholarly journals Orbital stability of solitary waves to the coupled compound KdV and MKdV equations with two components

2020 ◽  
Vol 5 (4) ◽  
pp. 3298-3320
Author(s):  
Xiaoxiao Zheng ◽  
◽  
Jie Xin ◽  
Yongyi Gu ◽  
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Stability Of Solitary Waves

Analytic and numerical nonlinear stability/instability of solitons for a Kawahara-like model

2016 ◽  
Vol 14 (04) ◽  
pp. 479-501
Author(s):  
José R. Quintero ◽  
Juan Carlos Muñoz
Keyword(s):  
Wave Velocity ◽  
Solitary Waves ◽  
Nonlinear Stability ◽  
Water Waves ◽  
Small Amplitude ◽  
Orbital Stability ◽  
Type Equation ◽  
Unstable Behavior ◽  
Stability Of Solitary Waves ◽  
Least Energy

We study orbital stability of solitary waves of least energy for a nonlinear Kawahara-type equation (Benney–Luke–Paumond) that models long water waves with small amplitude, from the analytic and numerical viewpoint. We use a second-order spectral scheme to approximate these solutions and illustrate their unstable behavior within a certain regime of wave velocity.

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