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The Inverse scattering transform fourier analysis for nonlinear problems
A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering. The form of each evolution… Expand
Complex Variables: Introduction and Applications
Part I. 1. Complex numbers and elementary functions 2. Analytic functions and integration 3. Sequences, series and singularities of complex functions 4. Residue calculus and applications of contour… Expand
Integrable nonlocal nonlinear Schrödinger equation.
A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and… Expand
Nonlinear-evolution equations of physical significance
We present the inverse scattering method which provides a means of solution of the initial-value problem for a broad class of nonlinear evolution equations. Special cases include the sine-Gordon… Expand
Method for Solving the Sine-Gordon Equation
On a new non-local formulation of water waves
The classical equations of water waves are reformulated as a system of two equations, one of which is an explicit non-local equation, for the wave height and for the velocity potential evaluated on… Expand
Two‐dimensional lumps in nonlinear dispersive systems
Two‐dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two‐dimensional nonlinear Schrodinger type equation. The amplitude of… Expand
Analytical and Numerical Aspects of Certain Nonlinear Evolution Equations
Nonlinear partial difference equations are obtained which have as limiting forms the nonlinear Schriidinger, Korteweg-deVries and modified Korteweg-deVries equations. These difference equations have… Expand
The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
Multiscale pulse dynamics in communication systems with strong dispersion management.
The evolution of an optical pulse in a strongly dispersion-managed fiber-optic communication system is studied. The pulse is decomposed into a fast phase and a slowly evolving amplitude. The fast… Expand