Abstract We present a new method for constructing exact solutions of nonlinear delay PDEs using special solutions of simpler auxiliary PDEs without delay. The application of the method is demonstrated on nonlinear reaction–diffusion and wave-type equations with delay that include variable coefficients and arbitrary functions. New generalized traveling-wave solutions and functional separable solutions in implicit form are obtained. Results of the paper can be used to formulate test problems intended to verify the adequacy and evaluate the accuracy of numerical and approximate analytical methods of solving the corresponding nonlinear initial-boundary value problems with delay.

中文翻译：

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一种构造非线性延迟偏微分方程精确解的方法

摘要 我们提出了一种使用更简单的无延迟辅助偏微分方程的特殊解来构造非线性延迟偏微分方程精确解的新方法。该方法在包括可变系数和任意函数的具有延迟的非线性反应-扩散和波型方程上的应用得到了证明。获得了隐式形式的新的广义行波解和函数可分解。论文的结果可用于制定测试问题，以验证其充分性并评估数值和近似解析方法在求解相应的具有延迟的非线性初边界值问题时的准确性。