Analyzing Sensitivity and Solitonic Behavior Using the Dullin-Gottwald-Holm Model in Shallow Water Waves

Abstract

This paper presents an investigation of traveling wave solutions and a sensitivity analysis for the unidirectional Dullin-Gottwald-Holm (DGH) system, a well-established model for wave propagation in shallow water. We apply the novel auxiliary equation method, a unique integration norm, to extract various soliton solutions, including kink, rational, bright, singular, and bright-singular solutions. Precise explicit solutions of the resultant ordinary differential equations are demonstrated using suitable parametric values. Furthermore, we explore the conditions that ensure the existence of these solutions. By applying the Galilean transformation, we convert the model into a planar dynamical system and evaluate its sensitivity performance. The selection of appropriate parameters enables the generation of two and three-dimensional sketches, as well as contour plots for each solution.

Analyzing Impact of Effort, Interest and Cognitive-Competence on Statistics Achievement Through Meditation of Self-Concept Statistics

“…Self-concept refers to an individual's beliefs and perceptions about their abilities, traits, and characteristics. Previous research has shown that self-concept can influence academic achievement [46,47]. Self-concept refers to an individual's perception of their abilities, characteristics, and values and has been found to be a crucial factor in academic achievement [48].…”

“…Students who have a positive self-concept tend to have a more positive attitude towards their academic work and are more motivated to achieve their goals [3]. Moreover, previous research has suggested that self-concept can mediate the relationship between cognitive competence and academic achievement [46,53]. This suggests that students who have higher cognitive competence may have a more positive self-concept, which, in turn, leads to better academic achievement.…”