9. (a) Use the Bcklund transformation (11.9.2ab) to show that four solutions u, (r=1,2,3,4) satisfy the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
9. (a) Use the Bäcklund transformation (11.9.2ab) to show that four solutions u, (r=1,2,3,4) satisfy the relation tan - (- (- - -)} = (2+2) - { (-4,-2) - { tan- a₁-a₂ where a₁ and 92 are nonzero constants. (b) Apply the relation in Exercise 9(a) to obtain a soliton solution of the sine-Gordon equation by setting u, 0, ₂ and u, different soliton solutions. 10. Examine the asymptotic nature of the two-soliton solution (11.10.19), as →∞. 11. Derive the solitary wave solution of the sinh-Gordon equation = sinh“. (1101) of the - (u - v), 2 1 1 1 = a sin u + b), u+ 0), = = sin - (u - ), (11.9.2ab) 2 لرحلية هذه إمارس 2 م ما الله -2 9. (a) Use the Bäcklund transformation (11.9.2ab) to show that four solutions u, (r=1,2,3,4) satisfy the relation tan - (- (- - -)} = (2+2) - { (-4,-2) - { tan- a₁-a₂ where a₁ and 92 are nonzero constants. (b) Apply the relation in Exercise 9(a) to obtain a soliton solution of the sine-Gordon equation by setting u, 0, ₂ and u, different soliton solutions. 10. Examine the asymptotic nature of the two-soliton solution (11.10.19), as →∞. 11. Derive the solitary wave solution of the sinh-Gordon equation = sinh“. (1101) of the - (u - v), 2 1 1 1 = a sin u + b), u+ 0), = = sin - (u - ), (11.9.2ab) 2 لرحلية هذه إمارس 2 م ما الله -2
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Evertight a leading manufacturer of quality nails produces 1 2 3 4 and 5 inch nails clavos for various uses In the production process if there is an overrun or the nails are slightly defective they...
-
Consider the MPS record below Wk 1 2 3 4 5 6 Forecast 15 25 9 15 22 5 Orders 7 10 10 10 Available ATP MPS On hand = 5, Lot size = 30 a. Complete the MPS record b. Update the record from part a -...
-
1. Determine the Cash Flow Erom Assets (FCF), Cash Flow to Creditors, and Cash Flow to Shareholders for the firm. 2. Assume you are sitting in a board meeting discussing the firm's plans for sales...
-
You are given the following information: The current gold price is $1,650, the net convenience yield for gold is 1.7% per year, the risk-free rate is 5% per year, the volatility is 30% per year, the...
-
A bank manager wants to know the mean amount owed on credit card accounts that become delinquent. A random sample of 100 delinquent credit card accounts taken by the manager produced a mean amount...
-
If a proton is moving at very high speed, so that its kinetic energy is much greater than its rest energy (m0c2), can it then decay via p n + +?
-
The following table lists values measured for 60 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration of the eruption (x1), the duration of the dormant...
-
1. What aspects of U.S. and Indian culture may have been causes of Cokes difficulties in India? 2. How might Coca-Cola have responded differently when this situation first occurred, especially in...
-
Below is a table with data about rising sea levels (sea levels as measured in New York relative to the level in 1900). Year Since 1900, t 0 25 50 75 100 125 Sea Level increase (mm), 0 60 140 240 310...
-
Consolidation related simulation example: Millennium Capital Management, Inc., (MCM) acquired a 90% interest in NextGen, Inc. MCM's Financial Manager, Matthew Steven, has prepared a draft memo to the...
-
A consultancy firm has three types of employees: part time interns, juniors and seniors. It is known that 2 0 % of the employees who are interns at the beginning of a period continue to be an intern,...
-
Opticians use the following thin-lens formula to perform calculations related to prescription lenses. = Use this formula to determine i when f= 18 cm and o= 24 cm. Round to the nearest cm.
-
An estate distributes an asset to its sole income beneficiary. The distribution wan, not a specific bequest. The basis of the asset to the estate is $1,000, and the asset's fair market value is...
-
DDD Ltd. is a private corporation with a taxation year ending on December 31. The sole shareholder is Donald Darwin Dorsey who is a Canadian resident throughout 2023. In 2023, DDD Ltd. had the...
-
Write the necessary python code to read the dataset file given to you and perform the following tasks: 1- Detect and list missing data in the dataset. Then fill these missing values with the suitable...
-
The process of obtaining funds from private parties such as investors, venture capital investors, or other companies interested in investing in a business is known as Question 3Answer a. loan...
-
Detailed Analysis - Show your work/calculations. Mr Muffler Garage is developing an operating budget for the month ending June 30, 2024. They expect to perform 800 repairs and maintenance during the...
-
As water moves through the hydrologic cycle, water quality changes are common because of natural phenomena or anthropogenic pollution. Using Figure 11.1, describe how water-quality changes occur...
-
(a) Apply the Gram-Schmidt Process to to find an orthogonal basis for W = span{x1, x2, x3}. (b) Use the result of part (a) to find a QR factorization of 0111 1110 0111 1110
-
In order for a linear system with augmented matrix [A ( b] to be consistent, what must be true about the ranks of A and [A ( b]?
-
Mark each of the following statements true or false: (a) If V = span(v1, . . . , vn), then every spanning set for V contains at least n vectors. (b) If {u, v, w} is a linearly independent set of...
-
Can we use the numerical integration methods discussed in this chapter to solve nonlinear vibration problems?
-
Houbolt method a. Assumes that acceleration varies linearly between \(t_{i}\) and \(t_{i}+\theta \Delta t ; \theta \geq 1\) b. Assumes that acceleration varies linearly between \(t_{i}\) and...
-
Express the following \(n\) th-order differential equation as a system of \(n\) first-order differential equations: \[a_{n} \frac{d^{n} x}{d t^{n}}+a_{n-1} \frac{d^{n-1} x}{d t^{n-1}}+\cdots+a_{1}...
Study smarter with the SolutionInn App