We consider nonlinear wave type PDEs with delay of the form $u_{tt}+H_1\left(u\right)u_t={\left[G\left(u\right)u_x\right]}_x+H_2\left(u\right)u_x+F(u,w),$where $u=u(x,t)$ is the unknown function, $w=u(x,t-\tau )$, and $\tau$ is the delay time. The source function $F(u,w)$ depends on one or several arbitrary functions of one argument. Using the modified method of functional constraints, we obtain a number of new exact solutions with generalized and functional separation of variables, as well as traveling-wave solutions. Most solutions are expressed in terms of elementary functions and contain free parameters. These solutions can be used to formulate test problems intended to evaluate the accuracy of numerical methods for solving nonlinear delay PDEs.

我们考虑具有以下形式的延迟的非线性波型PDE ${ü}_{ŤŤ}+H_{\mathrm{1个}}（ü）{ü}_{Ť}={\left[G（ü）{ü}_X\right]}_X+H_2（ü）{ü}_X+F（ü，w），$哪里 $ü=ü（X，Ť）$ 是未知函数 $w=ü（X，Ť-\tau ）$和 $\tau$是延迟时间。源函数$F（ü，w）$取决于一个参数的一个或多个任意函数。使用改进的功能约束方法，我们获得了具有变量的广义和功能分离的许多新的精确解，以及行波解。大多数解决方案都用基本函数表示，并包含自由参数。这些解决方案可用于制定测试问题，以评估求解非线性延迟PDE的数值方法的准确性。