A B€acklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has… (More)

The ‘tanh-coth expansion method’ for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic… (More)

Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant… (More)

The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form. On the other hand,… (More)

In a recent paper by Yaşar [E. Yaşar, New travelling wave solutions to the Ostrovsky equation, Appl. Math. Comput. 216 (2010), 3191–3194], ‘new’ travelling-wave solutions to the transformed reduced… (More)

An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the K(2, 2) equation (defocusing branch). Some known results in the… (More)

In a recent paper [Abazari R. Application of ( ′ G )-expansion method to travelling wave solutions of three nonlinear evolution equation. Computers & Fluids 2010;39:1957–1963], the (G/G)-expansion… (More)

None of our readers can be ignorant of the opinions of Dr. Snow on the communication of cholera by means of drinking water, nor of the perseverance and energy with which he has sought for facts to… (More)