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Publications Influence

The Inverse scattering transform fourier analysis for nonlinear problems

- M. Ablowitz, D. Kaup, A. Newell, H. Segur
- Mathematics
- 1 December 1974

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

2,196 99

Complex Variables: Introduction and Applications

- M. Ablowitz, A. Fokas
- Mathematics
- 1997

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

557 40- PDF

Integrable nonlocal nonlinear Schrödinger equation.

- M. Ablowitz, Z. Musslimani
- Physics, Medicine
- Physical review letters
- 7 February 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… Expand

323 35- PDF

Nonlinear-evolution equations of physical significance

- M. Ablowitz, D. Kaup, A. Newell, H. Segur
- Physics
- 9 July 1973

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

739 17

Method for Solving the Sine-Gordon Equation

- M. Ablowitz, D. Kaup, A. Newell, H. Segur
- Physics
- 1973

640 16

On a new non-local formulation of water waves

- M. Ablowitz, A. Fokas, Z. Musslimani
- Physics
- 1 September 2006

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

98 11- PDF

Two‐dimensional lumps in nonlinear dispersive systems

- J. Satsuma, M. Ablowitz
- Physics
- 1 July 1979

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

343 10

Analytical and Numerical Aspects of Certain Nonlinear Evolution Equations

- T. Taha, M. Ablowitz
- Physics
- 1984

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

149 10- PDF

The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems

- A. Fokas, M. Ablowitz
- Mathematics
- 1 February 1983

135 9

Multiscale pulse dynamics in communication systems with strong dispersion management.

- M. Ablowitz, G. Biondini
- Physics, Medicine
- Optics letters
- 1 November 1998

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

203 8- PDF