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113 papers
Exact trapped -soliton solutions of the nonlinear Schrödinger equation using the inverse problem method
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we show the application of the ``inverse problem'' method to construct exact trapped soliton-like solutions of the nonlinear Schrödinger or Gross-Pitaevskii equat…
Uniform Bose-Einstein Condensates as Kovaton solutions of the Gross-Pitaevskii Equation through a Reverse-Engineered Potential
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we consider a ``reverse-engineering'' approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevs…
A Solvable Model of a Nonlinear extension of Quantum Mechanics
Alan Chodos, Fred Cooper
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Ham…
Stability of exact solutions of the -dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter
Fred Cooper, Avinash Khare, Efstathios G. Charalampidis +2
In this work, we consider the nonlinear Schrödinger equation (NLSE) in dimensions with arbitrary nonlinearity exponent in the presence of an external confining potential.…
Stability of exact solutions of a nonlocal and nonlinear Schrödinger equation with arbitrary nonlinearity
Efstathios G. Charalampidis, Fred Cooper, Avinash Khare +2
This work focuses on the study of solitary wave solutions to a nonlocal, nonlinear Schrödinger system in + dimensions with arbitrary nonlinearity parameter . Although the…
Solitary wave solutions of the 2+1 and 3+1 dimensional nonlinear Dirac equation constrained to planar and space curves
Fred Cooper, Avinash Khare, Avadh Saxena
We study the effect of curvature and torsion on the solitons of the nonlinear Dirac equation considered on planar and space curves. Since the spin connection is zero for the curves…