Solitary Waves in Running Gases

Cover Solitary Waves in Running Gases
Solitary Waves in Running Gases
M C Shen
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Based upon this ansatz, we find the solution for the zero-th approximation as follows.
/. -.
bn p 'J, ^ tq "^^- l. -. O'i + .
„. QH " J (5. 6) subject to Pi = -^np^PQ - Pq f^(a, 0) =, Pi(a, r|g) =, where use is made of the fact that pQ, pQ, fQ and Uq are functions of •, -; only. Elimination of f, p, and u, from (;^. 6) and making use of (5. 5) yield the equation I (5-7) (ufpi. „). , - = Y '"'Pina' • I 00 The derivation of (5. 7) is deferred to Appendix I. From (3. 7) we have (5. 8) Pl^^ = --^
...^a'(a) CO and since Pi-(ct, t| ) = 0, we also obtain , X '?
[a . ( n r.
>•) (V^^) liK^'-a;'?, 1 vj, 0-?
wj.
-jfila SriB -12- (5. 9) P-Lp = ^a'(a)F(n), where a '(a) Is an arbitrary f-unctlon of c and Prom the last equation of (^^. 6) we have 1 ^-n+1 Pla ~ Jin PQ Pla = -k Po''"''^a'(a)P(ri), and Pi =^ p-"'^^a{a)P(ri) +b(ri) where ^^;e assiime a (a) ^ 0.


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