We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intemediat...

In a two-uid system where the lower uid is bounded below by a rigid bottom and the upper uid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical s...

We study the interaction of small amplitude, long-wavelength solitary waves in the Fermi–Pasta–Ulam model with general nearest-neighbour interaction potential. We establish global-in-time existence and stability of counterpropagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intermedia...

Exact periodic and solitary travelling-wave solutions of the short pulse equation are derived.

In this paper, based on the homogeneous balance principle and two improved projective Riccati Equations, exact solutions to the general form of BBM equation and the generalized BBM-Burgers equation with nonlinear terms of any order are obtained, which include several kinds of solitary wave solutions and periodic wave solutions. Some of them are found for the first time.

By adding a proper term to the Lagrangian density of a real non-linear KG system with a proposed non-topological unstable solitary wave solution, its stability guaranteed appreciably. This additional term in the new modified Lagrangian density behaves like a strong internal force which stands against any arbitrary small deformation in the proposed non-topological solitary wave solution.

By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the ...

Abstract In this work, we investigate for finding exact solitary wave solutions of the (2 + 1)-dimensional Zoomeron equation and the Tzitzeica–Dodd–Bullough (TDB) equation by using the direct algebraic method. The direct algebraic method is promising for finding exact traveling wave solutions of nonlinear evolution equations in mathematical physics. The competence of the methods for constructin...

This paper obtains the solitary wave, shock wave as well as singular soliton solutions to the generalized OstrovskyBenjamin-Bona-Mahoney (gO-BBM) equation. The ansatz method is applied to obtain the solutions. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions.

We find new analytic solitary-wave solutions of the higher order wave equations of Korteweg – De Vries (KdV) type (I), using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves are stable for wide ranges of the model coefficients. We study the dynamics of the two solitary-waves by using the analytic...