In this paper we derive some exact solutions for the Ito equation. These solutions are obtained by the sn-ns method, which is a generalization of the tanh-coth method.

The hyperbolic tangent (tanh) method is a powerful technique to symbolically compute traveling waves solutions of one-dimensional nonlinear wave and evolution equations. In particular, the method is well suited for problems where dispersion, convection, and reactiondiffusion phenomena play an important role. The technique is outlined for the computation of closedform tanh-solutions for nonlinea...

In [5] and [2] the authors describe the remarkable effectiveness of the doubly exponential ‘tanh-sinh’ transformation for numerical integration —even for quite unruly integrands. Our intention in this note is to provide a theoretical underpinning when the integrand is analytic for the observed superlinear convergence of the method. Our analysis rests on the corresponding but somewhat easier ana...

The nonlinear equations of mathematical physics are major subjects in physical science [1]. Recently many new approaches for finding the exact solutions to nonlinear wave equations have been proposed, for example, tanh-sech method [2–4], extended tanh method [5–7], sine-cosine method [8–10], homogeneous balance method [11, 12], Jacobi elliptic function method [13–16], F -expansion method [17–19...

In this paper, we investigate the new traveling wave solutions for sixth-order Boussinesq equation using tanh-coth method. Such a method is type of expansion that represents partial differential equations as polynomials $\tanh$ and $\coth$ functions. We discover several with different parameters, which are fundamental importance various applications.