Orbital stability of a two parameter family of solitary waves for a fourth order nonlinear Schrödinger type equation

2013 ◽  
Vol 54 (6) ◽  
pp. 061503 ◽  
Author(s):  
Jun-ichi Segata
Keyword(s):  
Solitary Waves ◽  
Fourth Order ◽  
Orbital Stability ◽  
Type Equation ◽  
Parameter Family ◽  
Nonlinear Schrödinger ◽  
Two Parameter

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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