Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D

2018 ◽  
Vol 382 (5) ◽  
pp. 300-308 ◽  
Author(s):  
T.I. Lakoba
Keyword(s):  
Solitary Wave ◽  
Numerical Study ◽  
Dirac Equations ◽  
Wave Stability ◽  
Nonlinear Dirac Equations

A Numerical Study on the Reflection of a Solitary Wave in Shallow Water

1982 ◽  
Vol 51 (3) ◽  
pp. 1018-1023 ◽  
Author(s):  
Mitsuaki Funakoshi ◽  
Masayuki Oikawa
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Numerical Study

scholarly journals Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Representation Formula ◽  
Critical Space ◽  
Lebesgue Spaces ◽  
Initial Value ◽  
Dirac Equations ◽  
Nonlinear Dirac Equations ◽  
Global Strong Solutions ◽  
Solution Representation

We study the initial value problem of some nonlinear Dirac equations which areLmℝcritical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solutionU∈L∞0,T; Ym+2ℝ.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

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