An analytical study on the existence of solitary structure at M = M-c

作者:Das Animesh*; Bandyopadhyay Anup; Das K P
来源:Journal of Plasma Physics, 2012, 78: 565-584.
DOI:10.1017/S0022377812000372

摘要

A general theory for the existence of solitary structure at M = M-c has been discussed, where M-c is the lower bound of the Mach number M, i.e., solitary structures start to exist for M %26gt; M-c. Three important results have been proved to confirm the existence of solitary structure at M = M-c. If V(phi)( V(M, phi)) denotes the Sagdeev potential with f being the perturbed field or perturbed dependent variable associated with a specific problem, V( M, f) is well defined as a real number for all M is an element of M and phi is an element of Phi(0), and V(M, 0) = V-%26apos;(M, 0) = V %26apos;%26apos;(M-c, 0) = 0, V%26apos;%26quot;(M-c, 0) %26lt; 0 (V%26quot;%26apos;(M-c, 0) %26gt; 0), partial derivative V/partial derivative M %26lt; 0 for all M(is an element of M) %26gt; 0 and phi(is an element of Phi(0)) %26gt; 0 (phi(is an element of Phi(0)) %26lt; 0), where %26apos;` partial derivative/partial derivative phi%26apos;, the main analytical results for the existence of solitary wave or double layer solution of the energy integral at M = M-c are as follows. Result 1: If there exists at least one value M-0 of M such that the system supports positive (negative) potential solitary waves for all M-c %26lt; M %26lt; M0, then there exists either a positive (negative) potential solitary wave or a positive (negative) potential double layer at M = M-c. Result 2: If the system supports only negative (positive) potential solitary waves for M %26gt; M-c, then there does not exist positive (negative) potential solitary wave at M = M-c. Result 3: It is not possible to have coexistence of both positive and negative potential solitary structures at M = M-c. Apart from the conditions of Result 1, the double layer solution at M = M-c is possible only when there exists a double layer solution in any right neighborhood of M-c. Finally, these analytical results have been applied to a specific problem on dust acoustic (DA) waves in non-thermal plasma in search of new results.

  • 出版日期2012-10