Elliptic solutions to a generalized BBM equation

Abstract

An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass' elliptic function $\wp$ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be expressed compactly in terms of the invariants of $\wp$. The approach unifies recently established ad-hoc methods to a certain extent. Evaluation of a balancing principle simplifies the application of this approach.

11 pages, 2 tables, submitted to Phys. Lett. A

References in corpus (3)

• Superposition in nonlinear wave and evolution equations
• Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
• 2-Soliton-solution of the Novikov-Veselov equation

Cited by in corpus (5)

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• Weierstrass traveling wave solutions for dissipative BBM equation
• Elliptic solutions and solitary waves of a higher order KdV--BBM long wave equation
• Periodic and solitary wave solutions to the Fornberg-Whitham equation
• A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems