Open AccessA nonlinear wave equation and exact periodic solutions in circular-rod waveguide
Author(s) -
Zhifang Liu,
Zhang Shan-yuan
Publication year - 2006
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.55.628
Subject(s) - nonlinear system , elliptic function , mathematical analysis , physics , trigonometric functions , nonlinear schrödinger equation , sinusoidal plane wave solutions of the electromagnetic wave equation , cross polarized wave generation , wave equation , classical mechanics , mathematics , electromagnetic wave equation , geometry , quantum mechanics , magnetic field , optical field
Under the condition of small deformation, a new nonlinear wave equation is derived to describe nonlinear wave evolution in a nonlinear elastic circular rod by means of Hamilton principle. The nonlinear constitutive relationship proposed by Cox and transverse Possion effects are simultaneously taken into account. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic cosine function expansion method. The exact periodic solutions of these nonlinear equations are obtained. The limiting conditions of these solutions are also given.