## Nonlinear Wave Equations

- C. Curtis, A. Dzhamay, W. Hereman, B. Prinari
- Mathematics
- 26 March 2015

where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F… Expand

## Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions

- B. Prinari, M. Ablowitz, G. Biondini
- Mathematics
- 29 June 2006

The inverse scattering transform for the vector defocusing nonlinear Schrodinger NLS equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated… Expand

## The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions

- F. Demontis, B. Prinari, C. Mee, F. Vitale
- Mathematics
- 1 July 2013

A rigorous theory of the inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonvanishing boundary values q±≡q0eiθ± as x→±∞ is presented. The direct problem is shown… Expand

## Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

- M. Ablowitz, G. Biondini, B. Prinari
- Mathematics
- 1 August 2007

The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been… Expand

## Soliton interactions in the vector NLS equation

- M. Ablowitz, B. Prinari, A. D. Trubatch
- Physics, Mathematics
- 1 August 2004

Collisions of solitons for two coupled and N-coupled NLS equation are investigated from various viewpoints. By suitably employing Manakov's well-known formulae for the polarization shift of… Expand

## The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

- G. Biondini, Daniel Kraus, B. Prinari
- MathematicsCommunications in Mathematical Physics
- 17 July 2015

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with… Expand

## Nonlinear Schrodinger systems: continuous and discrete

- M. Ablowitz, B. Prinari
- MathematicsScholarpedia
- 30 August 2008

## An integrable discretization of KdV at large times

- M. Boiti, F. Pempinelli, B. Prinari, A. Spire
- Mathematics, Physics
- 13 January 2001

An `exact discretization' of the Schrodinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation… Expand

## Integrable Nonlinear Schrodinger Systems and their Soliton Dynamics

- M. Ablowitz, B. Prinari, A. D. Trubatch
- Physics
- 2004

Nonlinear Schrodinger (NLS) systems are important examples of physically-significant nonlinear evolution equations that can be solved by the inverse scattering transform (IST) method. In fact, the… Expand

...

1

2

3

4

5

...