On a generalized Ablowitz–Kaup–Newell–Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

2017 ◽  
Vol 28 (3) ◽  
pp. 435-452 ◽  
Author(s):  
Sheng Zhang ◽  
Siyu Hong
Keyword(s):  
Wave Propagation ◽  
Soliton Solutions ◽  
Scattering Data

scholarly journals Dynamics of soliton solutions of the fifth-order nonlinear Schrödinger equation via the Riemann-Hilbert approach

2021 ◽  
Author(s):  
Jin-Jie Yang ◽  
Shou-Fu Tian ◽  
TIan-Tian Zhang ◽  
Xiao-Li Wang
Keyword(s):  
Inverse Scattering ◽  
Soliton Solutions ◽  
Scattering Data ◽  
Scattering Process ◽  
Nonlinear Schrödinger ◽  
Propagation Behavior ◽  
Direct Scattering ◽  
The One ◽  
New Phenomena ◽  
Fifth Order

The theory of inverse scattering is developed to investigate the initial-value problem for the fifth-order nonlinear Schrödinger (foNLS) equation under the zero boundary conditions at infinity. The spectral analysis is performed in the direct scattering process, including the establishment of the analytical, asymptotic and symmetric properties of the scattering matrix and the Jost functions. In the inverse scattering process, a suitable Riemann-Hilbert (RH) problem is successfully established by using the modified eigenfunctions and scattering data, and the relationship between the potential function and the solution of the RH problem is successfully established. In order to further analyze the propagation behavior of the solutions of the foNLS equation, we present some new phenomena of studying the one-, two-, and three- soliton solutions corresponding to simple zeros in scattered data. Finally, we also analyze the one- and two-soliton solutions corresponding to double zeros.

scholarly journals Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuan Li ◽  
Shou-Fu Tian
Keyword(s):  
Inverse Scattering ◽  
Hilbert Problem ◽  
Scattering Problem ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Scattering Data ◽  
Symmetric Relation ◽  
Hirota Equation ◽  
Direct Scattering ◽  
Scattering Transform

<p style='text-indent:20px;'>In this work, we study the inverse scattering transform of a nonlocal Hirota equation in detail, and obtain the corresponding soliton solutions formula. Starting from the Lax pair of this equation, we obtain the corresponding infinite number of conservation laws and some properties of scattering data. By analyzing the direct scattering problem, we get a critical symmetric relation which is different from the local equations. A novel left-right Riemann-Hilbert problem is proposed to develop the inverse scattering theory. The potentials are recovered and the pure soliton solutions formula is obtained when the reflection coefficients are zero. Based on the zero types of scattering data, nine types of soliton solutions are obtained and three typical types are described in detail. In addition, some dynamic behaviors are given to illustrate the soliton characteristics of the space symmetric nonlocal Hirota equation.</p>

Review Lecture - Water waves and their development in space and time

1985 ◽  
Vol 400 (1818) ◽  
pp. 1-18 ◽  
Keyword(s):  
Wave Propagation ◽  
Shallow Water ◽  
Deep Water ◽  
Water Waves ◽  
Water Wave ◽  
Hydraulic Jump ◽  
Soliton Solutions ◽  
Nonlinear Effects ◽  
Wave Fields ◽  
Turbulent Bore

Most practical predictions of water-wave propagation use linear approximations based on the concepts of ‘geometric’ rays and group velocity. Although this is successful, or adequate, in many instances, there are phenomena that can only be fully understood in terms of nonlinear effects. The recent boom in soliton-related studies has shed much light on the nonlinear aspects of wave propagation in shallow water. However, for waves on deeper water some of the nonlinear effects are only now being appreciated. A few, such as the focusing pattern of steady wave fields have direct parallels in shallow water; while others, such as deep-water soliton solutions, have their own rich structure. In deep or shallow water, wavebreaking is the most eye-catching development of a wave field. With the exception of the classical turbulent bore or hydraulic jump, our present models are still some way from giving a quantitative appreciation of important effects such as energy dissipation and momentum transfer, but causes of breaking for deep-water waves are now a little better understood.

On new closed form solutions: The (2+1)-dimensional Bogoyavlenskii system

2020 ◽  
pp. 2150150
Author(s):  
Kalim U. Tariq ◽  
Ali Zabihi ◽  
Hadi Rezazadeh ◽  
Muhammad Younis ◽  
S. T. R. Rizvi ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
Soliton Solutions ◽  
Coupled Model ◽  
Traveling Wave Solutions ◽  
Current Approach ◽  
Linear Wave ◽  
Closed Form Solutions ◽  
Linear Wave Propagation ◽  
Complex Models

This paper studies the new closed form solutions to (2+1)-dimensional Bogoyavlenskii system that describes interaction of a Riemann wave propagation. The extended Fan sub-equation technique is used to investigate some new traveling wave solutions to the higher-dimensional coupled model. The obtained closed form solutions are named as shock, kink, shock and periodic soliton solutions. Clearly, the outcomes of the study confirm the strength of the current approach. Moreover, the obtained results are helpful for the understanding of non-linear wave propagation and are of great interest to present-day scientists and can be employed to deal with more complex models arising in diverse disciplines of contemporary science.

Electron Microscopy of Shock Loaded Polycrystalline Beryllium

1974 ◽  
Vol 32 ◽  
pp. 506-507 ◽  
Author(s):  
J. M. Galbraith ◽  
L. E. Murr ◽  
A. L. Stevens
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Structural Change ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Shock Loading ◽  
Slip Systems ◽  
Compression Tests ◽  
X Ray Diffraction ◽  
X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

Sign in / Sign up

Export Citation Format

Share Document