It is common practice to describe propagation of one-dimensional acoustic waves in media possessing quadratic elastic nonlinearity and relaxation properties by the integro-differential equation [1] ((partial deriv) V)/((partial deriv) x) + α/(C_0~2) V (((partial deriv) V)/((partial deriv) τ)) = m/(2C_0) (partial deriv)/((partial deriv)τ) * ∫_(-∞)~τ ((partial deriv)V(τ_1))/((partial deriv)τ_1) exp (-(τ-τ_1)/T)dτ_1.
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机译:通常的做法是通过积分微分方程[1]((偏导数)V)/((偏导数)x)+α/()描述一维声波在具有二次弹性非线性和弛豫特性的介质中的传播。 C_0〜2)V(((偏导数)V)/((偏导数τ))= m /(2C_0)(偏导数)/((偏导数τ)*∫_(-∞)〜τ( (偏导数)V(τ_1)/((偏导数)τ_1)exp(-(τ-τ_1)/ T)dτ_1。
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