Nonlinear waves [electronic resource] : theory, computer simulation, experiment / M.D. Todorov.

The Boussinesq equation is the first model of surface waves in shallow water that considers the nonlinearity and the dispersion and their interaction as a reason for wave stability known as the Boussinesq paradigm. This balance bears solitary waves that behave like quasi-particles. At present, there...

Full description

Bibliographic Details
Uniform Title:IOP (Series). Release 5.
IOP concise physics.
Series on wave phenomena in the physical sciences.
Main Author: Todorov, Michail D. (Author)
Corporate Authors: Morgan & Claypool Publishers (Publisher)
Institute of Physics (Great Britain) (Publisher)
Language:English
Published: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2018]
Series:IOP (Series). Release 5.
IOP concise physics.
Series on wave phenomena in the physical sciences.
Subjects:
Nonlinear wave equations.
Mathematical physics.
Online Access:
IOP Concise Physics - Release 5: 2018 (IOPscience @ Institute of Physics)
Variant Title:
Nonlinear Waves: Theory, computer simulation, experiment
Format: Electronic eBook
Contents:
  • 1. Two-dimensional Boussinesq equation. Boussinesq paradigm and soliton solutions
  • 1.1. Boussinesq equations. Generalized wave equation
  • 1.2. Investigation of the long-time evolution of localized solutions of a dispersive wave system
  • 1.3. Numerical implementation of Fourier-transform method for generalized wave equations
  • 1.4. Perturbation solution for the 2D shallow-water waves
  • 1.5. Boussinesq paradigm equation and the experimental measurement
  • 1.6. Development and realization of efficient numerical methods, algorithms and scientific software for 2D nonsteady Boussinesq paradigm equation. Comparative analysis of the results
  • 2. Systems of coupled nonlinear Schrödinger equations. Vector Schrödinger equation
  • 2.1. Conservative scheme in complex arithmetic for vector nonlinear Schrödinger equations
  • 2.2. Finite-difference implementation of conserved properties of the vector nonlinear Schrödinger equation (VNLSE)
  • 2.3. Collision dynamics of circularly polarized solitons in nonintegrable VNLSE
  • 2.4. Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector nonlinear Schrödinger equation
  • 2.5. Repelling soliton collisions in vector nonlinear Schrödinger equation with negative cross modulation
  • 2.6. On the solution of the system of ordinary differential equations governing the polarized stationary solutions of vector nonlinear Schrödinger equation
  • 2.7. Collision dynamics of elliptically polarized solitons in vector nonlinear Schrödinger equation
  • 2.8. Collision dynamics of polarized solitons in linearly coupled vector nonlinear Schrödinger equation
  • 2.9. Polarization dynamics during takeover collisions of solitons in vector nonlinear Schrödinger equation
  • 2.10. The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled vector nonlinear Schrödinger equation
  • 2.11. Vector nonlinear Schrödinger equation with different cross-modulation rates
  • 2.12. Asymptotic behavior of Manakov solitons
  • 2.13. Manakov solitons and effects of external potential wells and humps 2-105
  • 3. Ultrashort optical pulses. Envelope dispersive equations
  • 3.1. On a method for solving of multidimensional equations of mathematical physics
  • 3.2. Dynamics of high-intensity ultrashort light pulses at some basic propagation regimes
  • 3.3. (3+1)D nonlinear Schrödinger equation
  • 3.4. (3+1)D nonlinear envelope equation (NEE)
  • 3.5. Summary of the studies.