Development of spreading symmetric two-waves motion for a family of two-mode nonlinear equations

Marwan Alquran; Imad Jaradat; Mohammed Ali; Nadeem Al-Ali; Shaher Momani

doi:10.1016/j.heliyon.2020.e04057

Development of spreading symmetric two-waves motion for a family of two-mode nonlinear equations

Heliyon. 2020 Jun 8;6(6):e04057. doi: 10.1016/j.heliyon.2020.e04057. eCollection 2020 Jun.

Authors

Marwan Alquran¹, Imad Jaradat¹, Mohammed Ali¹, Nadeem Al-Ali¹, Shaher Momani^{2

3}

Affiliations

¹ Department of Mathematics and Statistics, Jordan University of Science & Technology, Irbid 22110, Jordan.
² Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, United Arab Emirates.
³ Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan.

Abstract

In this work, a functional operator extracted from Korsunsky's technique is used to produce new two-mode nonlinear equations. These new equations describe the motion of two directional solitary-waves overlapping with an increasing phase-velocity and affected by two factors labeled as the dispersion and nonlinearity coefficients. To investigate the dynamics of this two-mode family, we construct the two-mode KdV-Burgers-Kuramoto equation (TMKBK) and two-mode Hirota-Satsuma model (TMHS). Two efficient schemes are used to assign the necessary constraints for existence of solutions and to extract them. The role of the phase-velocity on the motion of the obtained two-wave solutions is investigated graphically. Finally, all the obtained solutions are categorized according to their physical shapes.

Keywords: Applied mathematics; Computational mathematics; Kudryashov method; Mathematical analysis; Nonlinear physics; Solitary wave solutions; Tanh-coth-expansion method; Two-mode Hirota Satsuma; Two-mode KdV–Burgers–Kuramoto; Wave physics.