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Solitons, Nonlinear Evolution Equations and Inverse Scattering
1. Introduction 2. Inverse scattering for the Korteweg-de Vries equation 3. General inverse scattering in one dimension 4. Inverse scattering for integro-differential equations 5. Inverse scattering
Solitons and the Inverse Scattering Transform
Abstract : Under appropriate conditions, ocean waves may be modeled by certain nonlinear evolution equations that admit soliton solutions and can be solved exactly by the inverse scattering transform
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
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
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
Nonlinear differential–difference equations and Fourier analysis
The conceptual analogy between Fourier analysis and the exact solution to a class of nonlinear differential–difference equations is discussed in detail. We find that the dispersion relation of the
Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons
Preface Acknowledgements Part I. Fundamentals and Basic Applications: 1. Introduction 2. Linear and nonlinear wave equations 3. Asymptotic analysis of wave equations 4. Perturbation analysis 5. Water
Nonlinear differential−difference equations
A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact
A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II
It is known through the inverse scattering transform that certain nonlinear differential equations can be solved via linear integral equations. Here it is demonstrated ’’directly,’’ i.e., without the
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
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