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Nonlinear Wave Equations

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

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

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

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…
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Soliton interactions in the vector NLS equation

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

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…
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Nonlinear Schrodinger systems: continuous and discrete

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An integrable discretization of KdV at large times

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…
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Integrable Nonlinear Schrodinger Systems and their Soliton Dynamics

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…
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Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

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