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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… (More)

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… (More)

- Mark J. Ablowitz, Ziad H. Musslimani
- Physical review letters
- 2013

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… (More)

It is well known that the integrability (solvability) of a differential equation is related to the singularity structure of its solutions in the complex domain - an observation that lies behind the… (More)

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a… (More)

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… (More)

Various numerical methods are used in order to approximate the Korteweg-de Vries equation, namely: (i) Zabusky-Kruskal scheme, (ii) hopscotch method, (iii) a scheme due to Goda, (iv) a proposed local… (More)

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… (More)