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在求一类非线性波方程行波解时,先将有关的非线性常微分方程在其Poincaré相平面上作定性分析,然后再区别情况求积分,从而得到了各式各样的行波解。Progressive waves expressed by rational combination of elliptic functions in general and solitary waves, solitons and kinks in special cases are found as solutions to various nonlinear wave equations.
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