Orbital stability of solitary waves to the generalized Kdv equation with fifth order

2011 ◽  
Author(s):  
XiaoHua Liu
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Orbital Stability ◽  
Generalized Kdv Equation ◽  
Stability Of Solitary Waves ◽  
Fifth Order

Orbital stability of solitary waves for the compound KdV equation

2011 ◽  
Vol 12 (3) ◽  
pp. 1627-1639 ◽  
Author(s):  
Weiguo Zhang ◽  
Gaolong Shi ◽  
Yinghao Qin ◽  
Gongming Wei ◽  
Boling Guo
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Orbital Stability ◽  
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.

Interaction of solitary waves for the generalized KdV equation

2012 ◽  
Vol 17 (8) ◽  
pp. 3204-3218 ◽  
Author(s):  
Martin G. Garcia Alvarado ◽  
Georgii A. Omel’yanov
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Generalized Kdv Equation

scholarly journals EXISTENCE OF SOLITARY WAVES AND PERIODIC WAVES TO A PERTURBED GENERALIZED KDV EQUATION

2014 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Weifang Yan ◽  
Zhengrong Liu ◽  
Yong Liang
Keyword(s):  
Perturbation Theory ◽  
Solitary Waves ◽  
Wave Speed ◽  
Kdv Equation ◽  
Upper And Lower Bounds ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Periodic Waves ◽  
Regular Perturbation ◽  
Generalized Kdv Equation

In this paper, the existence of solitary waves and periodic waves to a perturbed generalized KdV equation is established by applying the geometric singular perturbation theory and the regular perturbation analysis for a Hamiltonian system. Moreover, upper and lower bounds of the limit wave speed are obtained. Some previous results are extended.

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
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