scholarly journals Deformation Anomalies Accompanying Tsunami Origination

2021 ◽  
Vol 9 (10) ◽  
pp. 1144
Author(s):  
Grigory Dolgikh ◽  
Stanislav Dolgikh
Keyword(s):  
Gordon Equation ◽  
Experimental Results ◽  
Tsunami Generation ◽  
Sine Gordon Equation ◽  
Laser Strainmeter ◽  
Underwater Landslide ◽  
Deformation Jump ◽  
Earth's Crust ◽  
The Many ◽  
The One

Basing on the analysis of data on variations of deformations in the Earth’s crust, which were obtained with a laser strainmeter, we found that deformation anomalies (deformation jumps) occurred at the time of tsunami generation. Deformation jumps recorded by the laser strainmeter were apparently caused by bottom displacements, leading to tsunami formation. According to the data for the many recorded tsunamigenic earthquakes, we calculated the damping ratios of the identified deformation anomalies for three regions of the planet. We proved the obtained experimental results by applying the sine-Gordon equation, the one-kink and two-kink solutions of which allowed us to describe the observed deformation anomalies. We also formulated the direction of a theoretical deformation jump occurrence—a kink (bore)—during an underwater landslide causing a tsunami.

TWO-BRANCH ENERGY OF MAGNETIC SURFACES AND CONNECTION WITH ANHOLONOMY

2000 ◽  
Vol 14 (19n20) ◽  
pp. 2083-2091
Author(s):  
RADHA BALAKRISHNAN
Keyword(s):  
Gordon Equation ◽  
Variational Equation ◽  
Curved Surfaces ◽  
General Boundary Conditions ◽  
Spin Vector ◽  
Sine Gordon Equation ◽  
Magnetic Surfaces ◽  
Soliton Lattice ◽  
Dependent Parameter ◽  
The One

For general boundary conditions, we show that the energy H of a classical Heisenberg ferromagnetic spin system on a curved surface satisfies the inequality H≥|Γ|. Here Γ is a certain geometric phase or anholonomy associated with the spin vector field. This is a generalization of the well known Bogomol'nyi inequality H≥4πQ (Q=integer). For a wide variety of curved surfaces, seeking solutions with certain symmetries, we find that the variational equation δH=0 can be reduced to a sine-Gordon equation with a geometry-dependent parameter. Soliton lattice solutions of this equation are analyzed. It is shown that both H and Γ develop two branches each, all of which merge at the one-soliton limit. This branching is interpreted as a topological transition of the spin textures that occurs at the one-soliton point.

scholarly journals Parametrically Driven One-Dimensional Sine-Gordon Equation and Chaos

1988 ◽  
Vol 43 (8-9) ◽  
pp. 727-733
Author(s):  
B. M. Herbst ◽  
W.-H. Steeb
Keyword(s):  
Driving Force ◽  
Gordon Equation ◽  
Zero Mode ◽  
Space Structure ◽  
Chaotic Behaviour ◽  
Force Frequency ◽  
Sine Gordon Equation ◽  
Mode Structure ◽  
One Dimensional ◽  
The One

AbstractThe chaotic behaviour of the parametrically driven one-dimensional sine-Gordon equation with periodic boundary conditions is studied. The initial condition is u(x, 0) = ƒ(x), ut (x, 0) = 0 where ƒ is the breather solution of the one-dimensional sine-Gordon equation at t = 0. We vary the amplitude of the driving force, the frequency of the driving force and the damping constant. For appropriate values of the driving force, frequency and damping constant chaotic behaviour with respect to the time-evolution of w(x = fixed, t) can be found. The space structure u(t = fixed, x) changes with increasing driving force from a zero mode structure to a breather-like structure consisting of a few modes.

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