This research analyses the impact of COVID-19 on the Spanish university system during the period of home lockdown put in place by the government of Spain between 15 March and 21 June 2020. This period did not involve a change to online teaching. Instead, it involved emergency remote teaching, wherein the content of face-to-face teaching was taught through non-classroom training using media, devices and tools available at that time. The main objective of the paper is related to the perceptions of students and teachers on emergency remote teaching regarding the face-to-face model. We applied statistical techniques of descriptive and inferential analysis over a sample of 2778 students and 221 teaching staff from the University of Cádiz. We also analysed the methodologies used, as well as the acquisition of skills, competencies and knowledge by the students in this situation, in order to detect whether this type of action can achieve sustainable education. This term refers to education that is capable of maintaining the continuous quality of the training of each student, who should acquire the required knowledge and competences regardless of unforeseen events. However, according to the results of this research, the sudden transition to e-learning, based on available technological and computer-based methods, did not guarantee sustainable education or its quality. This study establishes different possibilities for improving non-face-to-face teaching in this kind of situation. The results show greatly concerning levels of training and evaluation, as well as worse acquisition of skills. Both teachers and students declared a preference for face-to-face teaching. This perception should prompt the educational authorities to solve the existing problems in e-learning education, improving the transition and guaranteeing the sustainability of non-face-to-face education. This research highlights the areas for improvement in e-learning education in the ongoing situation, the general uncertainty in the transition, the lack of communication and the completion of a fair evaluation system. The results show that the methods used in this period must be improved to achieve sustainable teaching and learning during a pandemic. The results also emphasize the uncertainty in the educational community about the entire process. This study will help the educational authorities to improve the change of paradigm in higher education in the future.

For a generalized KdV-Burgers-Kuramoto equation we have studied conservation laws by using the multiplier method, and investigated its first-level and second-level potential systems. Furthermore, the Lie point symmetries of the equation and the Lie point symmetries associated with the conserved vectors are determined. We obtain travelling wave reductions depending on the form of an arbitrary function. We present some explicit solutions: soliton solutions, kinks and antikinks.

In this article, we show successful methods with a wider applicability in physics, which have been applied to make an analysis of generalized Drinfeld–Sokolov system. Lie’s classical symmetries have been calculated and they have given us the Lie-group classification depending on the parameters. Moreover, for each case we have obtained their optimal system and reductions to conclude obtaining traveling wave solutions using the sine–cosine method.