非线性LC电路方程的显式精确行波解

摘要

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.%　　理论上考察了具有耗散的非线性LC电路中的行波。借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程。一致地获得了丰富的显式精确解析行波解，包括精确冲击波解和奇异的行波解，和三角函数有理形式的周期波解。