Soliton solution of the osmosis K(2, 2) equation

In this Letter, by using the bifurcation method of dynamical systems, we obtain the analytic expressions of soliton solution of the osmosis K(2, 2) equation.Comment: 8 page

On Completely Integrability Systems of Differential Equations

In this note we discuss the approach which was given by Wazwaz for the proof of the complete integrability to the system of nonlinear differential equations. We show that his method presented in [Wazwaz A.M. Completely integrable coupled KdV and coupled KP systems, Commun Nonlinear Sci Simulat 15 (2010) 2828-2835] is incorrect.Comment: 14 pages. This paper was sent to the Communications in Nonlinear Science and Numerical Simulatio

Compactons and kink-like solutions of BBM-like equations by means of factorization

In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass function and its degenerated trigonometric and hyperbolic forms. Then, we obtain the pattern of periodic, solitary, compacton and kink-like solutions. We give also the Lagrangian and the Hamiltonian, which are linked to the factorization, for the nonlinear second order ordinary differential equations associated to the travelling wave equations.Comment: 10 pages, 8 figure

Elliptic solutions to a generalized BBM equation

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.Comment: 11 pages, 2 tables, submitted to Phys. Lett.

Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method

AbstractNew exact travelling wave solutions for the double sinh-Gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ODE method. The Painlevé property v = eu is employed to support the tanh method in deriving exact solutions. The work emphasizes the power of the methods in providing distinct solutions of different physical structures

Generalized (2+1)−dimensional breaking soliton equation

In this work, a general (2+1)-dimensional breaking soliton equation is investigated. The Hereman’s simplified method is applied to derive multiple soliton solutions, hence to confirm the model integrability.Publisher's Versio

The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations

AbstractThe complex modified K dV (CMK dV) equation and the generalized K dV equation are investigated by using the tanh method and the sine-cosine method. A variety of exact travelling wave solutions with compact and noncompact structures are formally obtained for each equation. The study reveals the power of the two schemes where each method complements the other