Show that u(x, t) = sech 2 (x t) satisfies the KortewegdeVries equation (which arises in

Question:

Show that u(x, t) = sech²(x − t) satisfies the Korteweg–deVries equation (which arises in the study of water waves):

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 17, 2024 03:00 AM

See More Questions

Many microorganisms propel themselves, at low Reynolds number, using undulatory motion. Examples include the helical motion of E. colis corkscrew tail (Box 14.3), and undulatory waves in a forest of...
Show that (9) in Sec. 12.6 with coefficients (10) is a solution of the heat equation for t > 0 assuming that f(x) is continuous on the interval 0 ¤ x ¤ L and has one-sided derivatives...
Waves of Arbitrary Shape. (a) Explain why any wave described by a function of the form y(x, t) = fix - ut) moves in the +x-direction with speed u. (b) Show that y(x, t) = f(x - ut) satisfies the wave...
A department store is being planned for a new shopping mall. Using the information in Table 4.8, assign departments to locations in order to minimize traffic flow through the store. TABLE 4.8...
Consider an oblique shock generated at a compression corner with a deflection angle = 18.2. A straight horizontal wall is present above the corner, as shown in Fig. 9.14. If the upstream flow has...
The Fara Littlebear Society is an NFPO funded by government grants and private donations. It was established in Year 5 by the friends of Fara Littlebear to encourage and promote the work of Native...
Use the following balance sheets and income statement to answer Required Use the indirect method to prepare the cash provided or used from operating activities section only of the statement of cash...
Cost of Assets, Subsequent Book Values, and Balance Sheet Presentation The following events took place at Tasty-Toppins Inc., a pizza shop that specializes in home delivery, during 2010: a. January...
E 5A Submit using Moodle in Assignments. 0 First Prepare; Current Assets and Current Liabilities, 2 Calculate Ratios Liquidity Ratios LO 3 BUSINESS APPLICATION The accounts and balances that follow...
This exercise shows that the hypotheses of Clairauts Theorem are needed. Let for (x, y) = (0,0) and f(0, 0) = 0. (a) Verify for (x, y) = (0,0): f(x, y) = xy- fx(x, y) = fy(x, y) = x - y x + y y(x4 +...
The Laplace operator is defined by = xx + yy . A function u(x, y) satisfying the Laplace equation u = 0 is called harmonic. Find all constants a, b such that u(x, y) = cos(ax)e by is harmonic.
The external auditors for Heart Health Procedures'(HHP) are currently performing the an nual audit of HHP's financial statements. As part of the audit, the external auditors have prepared a...
A pistoncylinder device contains 0.85 kg of refrigerant-134a at 210 oC. The piston that is free to move has a mass of 12 kg and a diameter of 25 cm. The local atmospheric pressure is 88 kPa. Now,...
3.3. Using the BEMT, show the effect of increasing linear twist on the variations in inflow, thrust, induced power, profile power, and lift coefficient across the span of a rotor with four blades of...
By uploading this work, I attest that the work contained herein is solely my own, that I only used the given equation sheet as a reference, and that I have not received any information from anyone...
Demand for patient surgery at Washington General Hospital has increased steadily in the past few years, as seen in the following table: ...
Explain product analysis
Jessie's Juice Bar prices its bottled juices by raising the wholesale price 50% and then adding 25. What is the wholesale price of a bottle of juice that sells for $2.95?
Consider a closed, rigid tank with a volume of 0.8L, filled with cold water initially at 27C. The tank is filled such that there are no voids (air pockets) within. The initial pressure within the...
Find the limit. lim V7 - 3x
Find the limit. Find each limit. x 4 5 + 1 lim >-1
Find the limit. lim (3x)(x 2)2]|
Nelo Partnership had three partners, whose capital balances on June 30 were as follows: Jack $50,000, Andy $35,000, Nick $22,000. The profit-sharing ratio is 6:4:2 (Jack, Andy, Nick). On July 1,...
Alex buys a Blu-ray disc costing $14.49. Use the table below to find the sales tax on this item. Amount of Sale ($) Tax ($) 13.70 13.89 0.69 13.90 14.09 0.70 14.10 14.29 0.71 14.30 14.49 0.72 14.50...
Show partial income statements through gross margin for all three methods, assuming both products are further processed into Current Attempt in Progress It's mind - boggling the number of products...

Show that u(x, t) = sech 2 (x t) satisfies the KortewegdeVries equation (which arises in

Question:

4u+ Uxxx +12uux = 0

Step by Step Answer:

Hence In Exercise 68 we found the following derivatives ux 2 sechx t t...View the full answer

Calculus

Students also viewed these Mathematics questions