物理学报
物理學報
물이학보
2013年
7期
15-23
,共9页
非线性LC电路%非线性耗散波动方程%冲击波%周期波
非線性LC電路%非線性耗散波動方程%遲擊波%週期波
비선성LC전로%비선성모산파동방정%충격파%주기파
nonlinear LC circuit%nonlinear dissipation wave equation%shock wave%periodic wave
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.
理論上攷察瞭具有耗散的非線性LC電路中的行波.藉助于作者最近髮展的精確求解非線性偏微分方程的擴展的雙麯函數方法解析地研究瞭模擬非線性電路中遲擊波的四階耗散非線性波動方程.一緻地穫得瞭豐富的顯式精確解析行波解,包括精確遲擊波解和奇異的行波解,和三角函數有理形式的週期波解.
이론상고찰료구유모산적비선성LC전로중적행파.차조우작자최근발전적정학구해비선성편미분방정적확전적쌍곡함수방법해석지연구료모의비선성전로중충격파적사계모산비선성파동방정.일치지획득료봉부적현식정학해석행파해,포괄정학충격파해화기이적행파해,화삼각함수유리형식적주기파해.
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.
