58 citations · 161 across the 9 of their papers we have counts for
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patt-sol1999★ 48 cited
Existence and stability of hole solutions to complex Ginzburg-Landau equations
Todd Kapitula, Jonathan Rubin
We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the…
patt-sol1997★ 58 cited
Stability criterion for bright solitary waves of the perturbed cubic-quintic Schroedinger equation
Todd Kapitula
The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger equation is considered. It is shown that in a certain region of parameter space these…
patt-sol1996★ 2 cited
Bifurcating bright and dark solitary waves of the nearly nonlinear cubic-quintic Schrodinger equation
Todd Kapitula
The existence of bright and dark multi-bump solitary waves for Ginzburg-Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are…