Related Experiment Video
Updated: Jan 1, 2026
08:19
Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
2.6K
Controllable symmetry breaking solutions for a nonlocal Boussinesq system
Jinxi Fei1, Zhengyi Ma2, Weiping Cao3
1Institute of Optoelectronic Technology, Lishui University, Lishui, 323000, China.
Scientific Reports
|December 25, 2019
Summary
This study explores a nonlocal Boussinesq system derived from coupled Alice-Bob systems. It reveals novel symmetry-breaking rogue wave, soliton, and breather solutions using advanced mathematical transformations.
Area of Science:
- Mathematical Physics
- Nonlinear Wave Phenomena
- Fluid Dynamics
Background:
- The generalized Boussinesq equation is a key model for describing water waves.
- Nonlocal systems offer new perspectives on wave dynamics beyond traditional models.
Purpose of the Study:
- To investigate a nonlocal Boussinesq system derived from coupled Alice-Bob (AB) systems.
- To explore novel solutions, including symmetry-breaking phenomena, within this nonlocal framework.
Main Methods:
- Reduction of the coupled AB systems via parity and time reversal symmetry.
- Application of an extended Bäcklund transformation.
- Derivation of the Hirota bilinear form to find exact solutions.
Main Results:
- Successfully obtained symmetry-breaking rogue wave solutions.
- Identified symmetry-breaking soliton and breather solutions.
- Analyzed residual and finite symmetry transformations of the nonlocal AB-Boussinesq system.
Conclusions:
- The study successfully derives and analyzes a novel nonlocal Boussinesq system.
- The findings demonstrate the existence of unique symmetry-breaking wave solutions.
- This research contributes to understanding complex wave behaviors in nonlinear systems.
Related Concept Videos
01:28Symmetry in Maxwell's Equations
4.1K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
4.1K
01:27Gauss's Law: Planar Symmetry
9.2K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.2K
01:26Transmission-Line Differential Equations
912
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
912
01:28Navier–Stokes Equations
2.0K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.0K
01:26Gauss's Law: Spherical Symmetry
8.9K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
8.9K
01:04Oscillations about an Equilibrium Position
6.5K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
6.5K