Propagation of proton solitons in hydrogen-bonded chains with an asymmetric double-well potential

Abstract

One of the most efficient ways of solving nonlinear partial differential equations is by an algebraic method such as the modified extended tangent hyperbolic function (METF) method aided by symbolic computation. We investigate the proton dynamics of a hydrogen-bonded (HB) chain with an asymmetric double-well potential based on a two-component soliton model. We solve the associated dynamical equations by invoking the METF method and explore the functional role of heavy ionic and protonic interactions in the nonlinear transport of protons in the form of kinkon, antikinkon, soliton and antisolitonic excitations.

Shape changing nonlocal molecular deformations in a nematic liquid crystal system

“…Most recently Soliman (Soliman, 2006) and El-Wakil (El-Wakil et al, 2005) modified the extended tanh-function method and obtained some new exact traveling wave solutions. We employ the modified extended tanh-function (METF) method (Soliman, 2006;El-Wakil et al, 2005;Kavitha et al, 2011bKavitha et al, , 2012 to solve the Eq. 12which governs the dynamics of director oscillations with elastic deformations such as splay, twist and bend.…”

Propagation of kink—antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes

“…Moreover, new solitary wave solutions may help to find new phenomena occurring in the microtubulin systems. Meantime powerful methods had been developed such as the Bäcklund transformation, [37] the Darboux transformation, [38] the inverse scattering transformation, [39] the bilinear method, [40] the generalized extended tangent hyperbolic function method, [41][42][43][44][45][46] the (G/G )-expansion method, [47] the sine-cosine method, [48] the homogeneous balance method, [49] the Riccati method, [50] the Jacobi elliptic function method [51][52][53] and the exp-function method, [54][55][56] etc to study the travelling wave solutions.…”

The propagation of shape changing soliton in a nonuniform nonlocal media

“…The wave phenomena observed in fluid dynamics, plasma physics, and chemical physics are often modelled by the bell-shaped and kink-shaped soliton solutions. During the last decades, effective methodologies such as inverse scattering method, [40,41] the tanh-sech method, [42] extended tanh method, [43][44][45][46][47][48][49][50][51] sinecosine method, [52][53][54][55][56] Jacobi elliptic function method, [57][58][59] and Hirota bilinear method [60,61] have been proposed for the determination of solitons. Among these proposed methods the tanh function method provides an effective and direct algebraic method for solving nonlinear equations.…”