We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DA...

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

We consider the soliton solutions in 1and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota’s method. We explicitly construct the solutions satisfying the boundary conditions. The Z∞-symmetric boundary condition can be introduced by the two-soliton solutions naturally. PACS number: 03.20+i, 02.60Lj

We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in its supersymmetry algebra. The bound is saturated by soliton solutions of first-order Bogomol'nyi-type equations. This generalizes results obtained previously for p = q models without torsion. We g...

We present a numerical study of essentially nonlinear dynamics surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation shear flow is known to have two branches; one which weakly dispersive for long waves. Weakly evolution the this branch can be described by Benjamin–Ono equation, integrable and has soliton multi-sol...

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the ”long wave limit” procedure of Ablowitz and Satsuma, and appropriate ”gauge” transformations. Their properties are also discussed and it is shown that these solutions interact elastically with...

We present the discovery of two types multiple-hump soliton modes in a highly dispersive optical fiber with Kerr nonlinearity. show that multi-hump solitons quartic or dipole are possible system presence higher-order dispersion. Such nonlinear wave packets very well described by an extended Schrödinger equation involving both cubic and dispersion terms. It is found third- fourth-order effects m...

Abstract A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota’s perturbation scheme. With the help of Maple, applying the approach to the (3 + 1)-dimensional ...

In this paper, we utilize the Riemann–Hilbert approach to discuss multi-soliton solutions of N-component nonlinear Schrödinger equations. Firstly, by transformed Lax pair, construct matrix-valued functions $$P_{1,2}$$ that satisfy analyticity and normalization corresponding jump matrix can be determined. Then, in reflectionless case, get $$q_{l}$$ $$(l=1,\ldots ,N)$$ equations, which are relate...