German cuisine widely available, but do not play an important role. Meat is usually braised; fried dishes also exist, but these recipes usually originate from France and Austria. Several cooking methods used to soften tough cuts have evolved into national specialties, including "Sauerbraten" (sour roast), involving marinating beef, horse meat or venison in a vinegar or wine vinegar mixture over several days. A long tradition of sausage-making exists in Germany; more than 1,500 different types of sausage () are made. Most "Wurst" is made with natural casings of pork, sheep or lamb intestines. Among the most popular and most common are "Bratwurst",
Slowly varying envelope approximation assumptions which are made need to be justified. For example, consider the electromagnetic wave equation: If k and "ω" are the wave number and angular frequency of the (characteristic) carrier wave for the signal "E"(r,"t"), the following representation is useful: where formula_3 denotes the real part of the quantity between brackets. In the "slowly varying envelope approximation" (SVEA) it is assumed that the complex amplitude "E"(r, "t") only varies slowly with r and "t". This inherently implies that "E"(r, "t") represents waves propagating forward, predominantly in the k direction. As a result of the slow variation of "E"(r, "t"), when