This article concerns  with  the  construction of the  analytical traveling  wave so- lutions  for the Generalized-Zakharov System  by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this  technique  in random  case by using random  traveling  wave trans- formation  in order  to  find what  is the  effect of the  randomness  input  for this  technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique.  The first moment of random solution is computed for different statistical probability distributions.

The PBL teaching method emphasizes using specific problems as a guide in practical application, guiding students to achieve better teaching implementation results in practice. The integration of cross-border e-commerce and English teaching is a practical English course content in the teaching of English majors. In the current stage of English course teaching, it is an important method that is innovative and targeted to improve students' English course learning effectiveness. In the specific application process, the application of PBL teaching method requires teachers to provide important support for improving the teaching effectiveness of cross-border e-commerce English courses under the PBL model by building educational and teaching training bases, actively providing sufficient practical education guidance platforms, and emphasizing the innovation and richness of teaching evaluation links.

The article examines the issues of application and improvement of the methodology for evaluating industrial enterprises as recipients of state support within the framework of the implementation of industrial policy. The authors considered approaches to the content of industrial policy, investigated the factors influencing its efficiency, identified aspects of its imperfections that arise when applying an incomplete list of important parameters of economic development and ambiguity in the interpretation of previously applied estimates. The article presents proposals to improve the methodology for assessing potential recipients of state support based on the development of a comprehensive indicator for assessing enterprises (recipients of support), taking into account not only the classical parameters of the economic efficiency of industrial enterprises applying for state financial assistance, but also such aspects as the development of budgetary funds, belonging to priority sectors of the economy, characteristics of sustainable development and export and innovation potential. Combining the results of a comprehensive assessment of the recipient of state support with a map of the business demography of the territory allows making a decision not only about the fact of support and its efficiency, but also to predict the assessment of the life cycle of the enterprise and its subsequent development.