Solitary wave solutions for a certain class of nonlinear differential equations

• Main Author: M.A. Abdel-Razek
• Format: Article
• Language: English
• Published: SpringerOpen 2011-10-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Nonlinear dispersive dissipative equations; Solitary wave solutions; A direct algebraic method; Pulse-type and kink-type solutions
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110256X11000241

Generalized forms of exact solitary wave solutions of the class (1.1) are investigated. The analysis rests mainly on the standard a direct algebraic method. The most general solutions are obtained, possibly having a constant term in their expansion into real exponentials. These solutions of the class (1.1) are performed under certain conditions for the relationship between the coefficients of the nonlinear, dispersive and dissipative terms. The analytical solutions of this class are of pulse-type and of kink-type solitary wave solutions and they are obtained with an arbitrary constant phase shift.