Orbital Stability of Solitary Waves for Generalized Ostrovsky Equation

2012 ◽  
pp. 423-428
Author(s):  
Dianchen Lu ◽  
Lili Liu ◽  
Li Wu
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Ostrovsky Equation ◽  
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 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.

Sign in / Sign up

Export Citation Format

Share Document