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Description
Semi-Classic Anal Nonlnr (2nd Ed)The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi classical limit before the formation of caustics. The second part treats the semi classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three
The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.
Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schr
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4.8 ★★★★★
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Product Reviews
★★★★★ 5
Sturdy, high quality, and protective
Color: Green, Size: 15-inch for New MacBook Air
This is my third TomToc laptop sleeve. Each time, I bought another, less expensive brand first and returned it. TomToc offers the best protection in a soft-shell sleeve.
Immediately when you open it, you feel the higher quality material and density. It’s not heavy, but it is thick padded and doesn’t easily bend with pressure. The zipper is built to last, sturdy, and easy to operate without that chintzy feeling from cheap zippers.
If you pay attention to the construction, you quickly see why it’s about double in price. There is an inner pad to protect the laptop from not just drops and shock, but also from the zipper. The corners are reinforced and add extra protection. It is definitely worth double the price.
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Reviewed in the United States on April 11, 2026
★★★★★ 5
Great Protection
Color: Orange, Size: 13-inch for New MacBook Air & Pro
This is a very nice, protective case. The material is thick and cushions the laptop great! Computer fits nice and cozy; great fit. I love the bright orange! I highly recommend.
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Reviewed in the United States on April 23, 2026
★★★★★ 5
A sold, attractive, case.
Color: Navy Blue, Size: 13-inch for New MacBook Air & Pro
This case looks great, has a nice, lively color scheme, and seems to be reasonably protective and sturdy. I wouldn’t toss a laptop around with only this as protection, but I feel fairly confident in it for small drops. The fabric is easy to clean and has held up well. You can charge without taking it out of the case thanks to a zipper, and it doesn’t add much bulk, making it quite portable. All in all a good balance of protection, cost, and style.
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Reviewed in the United States on June 2, 2026
★★★★★ 5
I would rescue it from a fire even if it were empty. I'm kidding but I do like this sleeve a lot.
Color: Orange, Size: 13-inch for New MacBook Air & Pro
Fits perfectly. Superb padding. The corner padding inspires confidence-not that I want to test it! The orange color is-chef's kiss-beautiful. A perfect contrast to the midnight color of my MacBook. I could gush about that stuff all day. But you all want to know about the other stuff.
Zippers: Two YKK no snag bi-directional closers for the main opening and a solo no snag YKK for the side pocket.
Outside: Feels like tactical nylon type fabric. I haven't and won't intentionally test its stain resistance. But I suspect it would clean up just fine.
Interior: A very soft microfiber like interior covering an odor free padding that is firm yet forgiving. There is a recess you push your laptop into making for a snug fit that, like I wrote earlier, inspires confidence. This sleeve is larger than some competing brands but seeing the recess in person explains why.
Having touched on the size of this sleeve, it maintains the svelteness of my MacBook Air. Yes, it is thicker than some other sleeves, by a smidge. However the additional protection suggested but that smidge, that minute extra ish is worth it to me. The sleeve fits in my travel backpack, so that's all good.
Lastly, I would consider putting a tablet or phone in the sidepocket but not anything that would concentrate the any energy that dissipates during a fall. Had I designed this product I wouldn't have included the side pocket. It's great for documents and thin things but the sell page suggests chargers. That seems like inviting risk. You do you.
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Reviewed in the United States on January 22, 2026
★★★★★ 4
Better Lips, Better Fit, Less Nonsense
Color: Black, Size: 13-inch for New MacBook Air & Pro
I tested this sleeve with a 13.6” MacBook Air (M4), and the difference is immediately noticeable.
First thing: fit. This one actually holds the laptop in place. The padded “lips” in the corners create just enough resistance that you have to guide the MacBook in and out. It’s not a loose drop-in like other cases — it feels controlled. If I shake it, there’s barely any movement, which is exactly what I was looking for.
Second: build quality. The stitching is clean and consistent — almost surgical compared to the wrinkled mess I saw on another model. The outer fabric stays flat, no weird waves or cheap-looking folds. The interior lining is softer and thicker too, so it feels more protective without being bulky.
Third: structure. I even did a quick “real-world” test — stood it vertically on a mattress, zipper open, applied pressure from the top — and it held its shape. The other case I tried would have collapsed immediately. This one actually feels like it can handle normal use without transferring pressure straight into the laptop.
The external pocket is simple but practical. It fits the charger brick and cable without interfering with the main compartment, which keeps the laptop fit intact.
Only downside: I could do without the orange accents. A full black version would be perfect. But honestly, that’s cosmetic — functionally, this one does what it’s supposed to do.
At around this price point, this feels fair. Not luxury, not overhyped — just a well-executed, practical sleeve that gets the fundamentals right.
Bottom line: not perfect, but finally something that feels properly made and actually holds the laptop instead of just surrounding it.
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Reviewed in the United States on March 29, 2026