Existence and stability of a two-parameter family of solitary waves for a logarithmic NLS–KdV system

2019 ◽  
Vol 189 ◽  
pp. 111563 ◽  
Author(s):  
Alex H. Ardila
Keyword(s):  
Solitary Waves ◽  
Parameter Family ◽  
Existence And Stability ◽  
Two Parameter

Existence and stability of ground-state solutions of a Schrödinger—KdV system

2003 ◽  
Vol 133 (5) ◽  
pp. 987-1029 ◽  
Author(s):  
John Albert ◽  
Jaime Angulo Pava
Keyword(s):  
Time Dependence ◽  
Ground State ◽  
Nonlinear Waves ◽  
Ground States ◽  
Energy Functional ◽  
Parameter Family ◽  
Existence And Stability ◽  
Image Position ◽  
Range Of Values ◽  
Two Parameter

We consider the coupled Schrödinger–Korteweg–de Vries system which arises in various physical contexts as a model for the interaction of long and short nonlinear waves. Ground states of the system are, by definition, minimizers of the energy functional subject to constraints on conserved functionals associated with symmetries of the system. In particular, ground states have a simple time dependence because they propagate via those symmetries. For a range of values of the parameters α, β, γ, δi, ci, we prove the existence and stability of a two-parameter family of ground states associated with a two-parameter family of symmetries.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter
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