# How do you solve the sine-Gordon equation?

## How do you solve the sine-Gordon equation?

A numerical scheme

1. A numerical scheme. Consider an IVP for the sine-Gordon equation (5.1):
2. utt −uxx +sin(u) = 0. on the interval x ∈ [a, b] with initial conditions.
3. u(x,0) = f(x), ut(x,0) = g(x),
4. (5.8) and with, e.g., no-flux boundary conditions.

What is breather solution?

A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon equation and the focusing nonlinear Schrödinger equation are examples of one-dimensional partial differential equations that possess breather solutions.

What is a kink solution?

Kink waves are solitons that rise or descend from one asymptotic state to another, and hence another type of traveling waves as in the case of the Burgers hierarchy. Peakons, that are peaked solitary wave solutions, are another type of travelling waves as in the case of Camassa-Holm equation.

### What is the difference between soliton and solitary wave?

Mathematically, there is a difference between solitons and solitary waves. Solitons are localized solutions of integrable equations, while solitary waves are localized solutions of non-integrable equations. For this reason, they are sometimes called soliton-like excitations.

What is the Gordon equation?

The Gordon Equation states that the long-term expected real (inflation adjusted) return from the market should approximate the inflation-adjusted compound yearly growth rate in dividends plus the current dividend yield.

What is kink soliton?

The 1-soliton solution for which we have chosen the positive root for is called a kink and represents a twist in the variable which takes the system from one solution to an adjacent with . The states are known as vacuum states, as they are constant solutions of zero energy.

## What is a soliton in physics?

A soliton is a solitary wave that behaves like a “particle”, in that it satisfies the following conditions (Scott, 2005): It must maintain its shape when it moves at constant speed. When a soliton interacts with another soliton, it emerges from the “collision” unchanged except possibly for a phase shift.

What are soliton solutions?

Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland.

Are tsunamis solitons?

The waves pass through each other with very small ultimate deformation. Tsunamis behave like solitons with very large wavelength. There is no point trying to send a counter wave to neutralize one. Rogue waves also are to solitons.

### Which is the formula of Gordon’s model of dividend policy?

Gordon’s model is one of the most popular mathematical models to calculate the market value of the company using its dividend policy….Relation of Dividend Decision and Value of a Firm.

Relationship between r and k Increase in Dividend Payout
r

Price per share increases
r=k No change in the price per share

How do you calculate Gordon growth rate?

#1 – Gordon Growth Model Formula with Constant Growth in Future Dividends

1. Here,
2. Growth Rate = Retention Ratio * ROE.
3. r = (D / P0) + g.
4. Find out the stock price of Hi-Fi Company.
5. Here, P = Price of the Stock; r = required rate of return.
6. Big Brothers Inc.
7. Find out the price of the stock.

What is singular soliton?

In 2D, the NLSE with a quintic self-focusing term admits singular soliton solutions with intrinsic vorticity too, but they are fully unstable. We also mention that dissipative singular solitons can be produced by the model with a complex coefficient in front of the nonlinear term.

## What is a sine Gordon breather?

Sine-Gordon standing breather is a swinging in time coupled kink-antikink 2-soliton solution. Large amplitude moving sine-Gordon breather. A breather is a localized periodic solution of either continuous media equations or discrete lattice equations.

What is a breather in physics?

A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon equation and the focusing nonlinear Schrödinger equation are examples of one- dimensional partial differential equations that possess breather solutions.

What is a breather pseudospherical surface?

This breather pseudospherical surface corresponds to a solution of a non-linear wave-equation. Sine-Gordon standing breather is a swinging in time coupled kink-antikink 2-soliton solution. Large amplitude moving sine-Gordon breather.

### What is a discrete breather solution?

Breather. A discrete breather is a breather solution on a nonlinear lattice . The term breather originates from the characteristic that most breathers are localized in space and oscillate ( breathe) in time. But also the opposite situation: oscillations in space and localized in time [clarification needed], is denoted as a breather.

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