Open AccessExplicit and exact traveling wave solutions to the nonlinear LC circuit equation
Author(s) -
Yadong Shang,
Yong Huang
Publication year - 2013
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.62.070203
Subject(s) - nonlinear system , physics , dissipation , trigonometric functions , partial differential equation , mathematical analysis , shock wave , hyperbolic function , traveling wave , wave propagation , sinusoidal plane wave solutions of the electromagnetic wave equation , classical mechanics , electromagnetic wave equation , mathematics , mechanics , quantum mechanics , geometry , optical field , magnetic field
Traveling wave in a nonlinear LC circuit with dissipation have been investigated theoretically. With the aid of the extended hyperbolic function method,developed by the authors in recent works to solve nonlinear partial differential equations exactly, the fourth order nonlinear wave equation with dissipation, which models shock wave propagation in a nonlinear LC circuit, have been analytically studied. Abundant explicit and exact traveling wave solutions to the fourth order nonlinear wave equation with dissipation are obtained. These solutions include exact shock wave solutions, singular traveling wave solutions, and periodic wave solutions in a rational form of trigonometric functions.